UC-NRLF 


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OF  THE 

JNIVERS1TY 

OF 


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CONDENSATION  OF  VAPOR  AS  INDUCED 
BY  NUCLEI  AND  IONS 


THIRD  REPORT 


BY  CARD  BARUS 

Hazard  Professor  of  Physics^T^rown  University 


WASHINGTON,  D.  C.: 

Published  by.  the  Carnegie  Institution  of  Washington 
1908 


CONDENSATION  OF  VAPOR  AS  INDUCED 
BY  NUCLEI  AND  IONS 


THIRD  REPORT 


BY  CARL  BARUS 

Hazard  Professor  of  Physics,  Brown  University 


WASHINGTON,  D.  C.: 

Published  by  the  Carnegie  Institution  of  Washington 
1908 


CARNEGIE  INSTITUTION  OF  WASHINGTON 
PUBLICATION  No.  96 


aSSICS  UBRARY 


^.  7  1 


U  BRAKY 


PREFA'CE. 


In  the  following  report  I  have  given  an  account  of  experiments  made 
with  a  plug-cock  fog  chamber  during  the  last  year  and  a  half. 

The  first  chapter  summarizes  the  equations  frequently  needed  and 
adds  other  important  suggestions  relating  to  the  efficiency  of  the  ap- 
paratus used  for  condensation  of  water  vapor  suspended  in  air. 

I  have  adduced,  in  Chapter  II,  the  results  of  a  long  series  of  experi- 
ments begun  May  9,  1905,  to  determine  whether  the  colloidal  or  vapor 
nucleations  of  dust-free  air  show  any  interpretable  variations  in  the 
initial  regions  (ions),  which  would  correspond  to  variations  of  a  natural 
radiation  entering  the  chamber  from  without.  The  fog-chamber  method 
seems  to  be  too  complicated  to  give  trustworthy  indications  of  such 
changes  of  ionization  as  have  been  since  discovered  with  the  aid  of  the 
electrical  method  by  Wood  and  Campbell.  An  interesting  result,  how- 
ever, came  out  of  the  experiments  in  question,  as  a  whole,  showing  that 
the  vapor  nucleation  is  variable  with  temperature  in  the  region  exam- 
ined to  the  extent  of  about  2  per  cent  per  degree. 

The  fog  chamber  used  in  the  present  research  having  undergone 
varied  modifications  since  the  coronas  were  last  standardized  (1904), 
it  seemed  necessary  to  repeat  the  work  for  the  present  report.  This 
was  particularly  necessary  because  the  subsequent  investigations  were 
to  depend  essentially  on  the  values  of  the  nucleation  observed.  These 
comparisons  are  shown  in  Chapters  III  and  IV.  In  the  former  the 
diffractions  are  obtained  from  a  single  source  of  light  and  the  angular 
diameter  of  the  coronas  is  measured  by  a  goniometer;  in  the  latter  the 
fiducial  annuli  of  two  coronas  due  to  identical  sources  of  light  are  put 
in  contact  and  the  distance  apart  of  the  lamps  is  measured  under  known 
conditions.  This  contact  method  has  many  advantages  and  above  all 
admits  of  the  use  of  both  eyes.  In  both  cases,  moreover,  the  nucleation 
of  dust-free  air,  in  the  presence  as  well  as  in  the  absence  of  penetrating 
artificial  radiation,  is  redetermined.  All  results  agree  among  them- 
selves and  with  the  older  work,  as  closely  as  may  be  expected  in  work  of 
the  present  kind,  below  the  middle  green-blue-purple  corona  (usually 
corresponding  to  io5  nuclei);  but  above  this  there  is  much  divergence, 
which  will  probably  not  be  overcome  until  some  means  for  keeping  the 
air  rigorously  homogeneous  in  nucleation  throughout  a  given  series  of 
experiments  has  been  devised. 

Chapter  V  contains  some  remarkable  results  on  the  properties  of 
nuclei  obtained  from  the  evaporation  of  fog  particles.  It  will  be  seen 


in 


M663474 


IV  PREFACE. 

that  such  residual  water  nuclei  behave  very  differently,  according  as 
the  precipitation  takes  place  on  solutional  nuclei  like  those  of  phos- 
phorus, or  upon  the  vapor  nuclei  of  dust-free  wet  air,  or  upon  the  ions; 
80  per  cent  of  the  nuclei  may  vanish  in  the  first  evaporation  in  the 
latter  case,  fewer  in  the  second  case,  and  none  in  the  first. 

In  Chapter  VI  the  endeavor  is  made  to  standardize  the  coronas  by 
aid  of  the  decay  constants  of  the  ions  as  found  by  the  electrical  method. 
The  curious  result  follows  that  in  order  to  make  these  data  agree  with 
those  of  Chapters  III  and  IV  it  is  necessary  to  assume  an  absorption 
of  nuclei  varying  as  the  first  power  of  their  number  as  well  as  a  decay 
by  their  mutual  coalescence.  If  a  be  the  number  of  nuclei  (ions)  gen- 
erated per  second  by  the  radiation,  b  the  number  decaying  per  second, 
and  c  the  number  absorbed  per  second,  the  equation  dn/dt  =  a  +  bn2-{-cn 
is  suggested. 

My  thanks  are  due  to  Miss  L.  B.  Joslin,  who  not  only  assisted  me  in 
many  of  the  experiments  requiring  two  observers,  but  lent  me  efficient 
aid  in  preparing  the  manuscripts  and  drawings  for  the  press. 

CARL  BARUS, 

BROWN  UNIVERSITY,  July,  1907. 


CONTENTS. 

CHAPTER  I. — Efficiency  of  the  Plug-cock  Fog  Chamber. 

1 .  Introduction T 

2.  The  variables.     Table  i x 

3.  Approximate  computations  of  />x  and  p2.     Table  2;  fig.  i 3 

4.  Definite  computations  of  pt  and  p2.     Table  3 6 

5.  Computation  of  vjv.     Table  3 ;  fig.  2 7 

6.  Approximate  computation  of  j^ 8 

7.  Approximate  computation  of  p2 9 

8.  Rate  of  reheating  of  the  j:og_chamber.    Table  4;  fig.  3 Io 

9.  Definite  computation  of  rlt  plt  r2,  £2,  etc.     Table  5 ll 

10.  Conclusion X3 

CHAPTER  II. — Changes  of  Vapor  Nucleation  of  Dust-free  Wet  Air  in  Lapse 
of  Time,  together  with  Effects  of  the  Limits  of  Pressure  between  which 
a  given  Drop  Takes  Place,  on  the  Efficiency  of  the  Fog  Chamber. 

n.  Introduction.     Table  6;  fig.  4 J4 

12.  Data.     Tables  7  and  8 ;  figs.  5  and  6 J7 

13.  Explanation.     Table  9 2l 

14.  The  effect  of  vapor  pressure.     Table  9;  fig.  7 22 

15.  New  data  for  vapor  nucleation  in  lapse  of  time.    Tables  10  and  1 1 ;  figs.  8,  a,  b  .  .  24 

16.  Effect  of  barometer 33 

17.  Effect  of  temperature 33 

18.  Effect  of  ionization.     Table  12 ;  fig.  9 33 

19.  Mean  results.     Tables  13  and  14,  fig.  10 36 

20.  Nucleations  depending  upon  dp/p.     Table  15 37 

21.  Possible  suggestions  as  to  the  temperature  effect 39 

22.  Another  suggestion 41 

23.  Conclusion 4 l 

CHAPTER  III. — The  Nucleation  Constants  of  Coronas. 

RESULTS  WITH   A   SINGLE   SOURCE   OF  LIGHT. 

24.  Introduction 43 

25.  Apparatus  and  methods.     Fig.  1 1 43 

26.  Equations  and  corrections.     Tables  16  and  17;  figs.  12  and  13 45 

27.  Data  for  moderate  exhaustions 49 

28.  Remarks  on  the  tables  and  charts 49 

29.  Data  for  low  exhaustions.     Table  18;   figs.  14  and  15 51 

30.  Data  for  high  exhaustions.     Table  19;  fig.  16 54 

31.  Standardization  with  ions 56 

32.  Further  data.     Table  20;    figs.  17  and  18 56 

33.  The  violet  and  green  coronas.     Tables  21  and  22;   fig.  19 59 

34.  Insertion  of  new  values  for  m.     Table  23 61 

35.  Wilson's  data  and  conclusions.     Table  24 62 

36.  Longer  intervals  between  observations.     Conclusion 63 

DISTRIBUTIONS  OF  VAPOR  NUCLEI  AND  OF  IONS  IN  DUST-FREE  WET  AIR.     CON- 
DENSATION AND  FOG   LIMITS. 

37.  Introductory 65 

38.  Notation 65 

39.  Data.     Tables  25,  26,  27,  28,  and  29 65 

v 


VI  CONTENTS. 

Page 

40.  Graphs.     Dust-free  air.     Figs.  20,  21,  and  22 68 

41 .  Weak  radiation 7° 

42.  Moderate  radiation 7° 

43.  Strong  radiation 7° 

44.  Other  nucleations 7° 

45.  Temperature  effects.     Table  30 7 l 

46.  New  investigations.     Tables  31,  32,  and  33;    fig.  23 72 

47.  Conclusion 75 

CHAPTER  IV. — The  Nucleation  Constants  of  Coronas. — Continued. 

ON   A   METHOD   FOR  THE   OBSERVATION   OF  CORONAS. 

48.  Character  of  the  method.     Fig.  24 76 

49.  Apparatus 77 

50.  Errors.     Table  34;  fig.  25 77 

51.  Data.     Table  35 78 

52.  Remarks  on  the  tables  and  conclusion.    Table  36;  fig.  26 81 

DISTRIBUTIONS  OF  VAPOR  NUCLEI  AND  IONS  IN  DUST-FREE  WET  AIR. 

53.  Behavior  of  different  samples  of  radium.     New  fog  chamber 84 

54.  Data.     Table  37 ;  fig.  27 84 

55.  Distributions  of  vapor  nuclei  and  ions.    Tables  38  and  39;   figs.  28  and  29..  .  87 

56.  Remarks  on  the  table 88 

57.  Condensation  limits  and  fog  limits.     Conclusion 90 

CHAPTER  V. — Residual  Water  Nuclei. 

PROMISCUOUS   EXPERIMENTS. 

58.  Historical 92 

59.  Purpose,  plan,  and  method 93 

60.  Residual  water  nuclei  after  natural  evaporation  of  fog  particles.    Table  40.  .  94 

61.  Rapid  evaporation  of  fog  particles.     Table  41 ;    fig.  30 95 

62.  Continued.     Tables  42  and  43 ;  fig.  31 98 

63.  Persistence  of  water  nuclei.    Table  44;    fig.  32,  a,  b 103 

64.  Summary 104 

THE   PERSISTENCE   OF   WATER   NUCLEI   IN   SUCCESSIVE   EXHAUSTIONS. 

65.  Standardization  with  ions.     Table  45;  fig.  33 105 

66.  Further  data.     Tables  46  and  47 ;  fig.  34,  a,  b,  c 106 

67.  Data  for  vapor  nuclei 1 1 1 

68.  Remarks  on  tables.    Table  48;  figs.  35,  36,  a,  b,  c,  d,  e,  f,  and  37,  a,  b,  c,  d  .  .  in 

69.  Loss  of  nuclei  actually  due  to  evaporation.    Table  49;   figs.  38  and  39 117 

70.  Conclusion 1 20 

CHAPTER  VI. — The  Decay  of  Ionized  Nuclei  in  the  Lapse  of  Time. 

7 1 .  Introduction 1 2 1 

72.  Data.     Table  50;  fig.  40 121 

73.  Exhaustions  below  condensation  limit  of  dust-free  air.     Table  51 ;  fig.  41 124 

74.  Data  for  weak  ionization.     Table  52 125 

75.  Further  experiments.     Table  53;  figs.  42,  43,  and  44 128 

76.  Case  of  absorption  and  decay  of  ions 128 

77.  Absorption  of  phosphorus  nuclei.     Table  54 130 

78.  Data.     Table  55;   figs.  45  to  49 134 

79.  Remarks  on  tables.     Tables  56  and  57 135 

80.  Conclusion 


CHAPTER   I. 
EFFICIENCY  OF  THE  PLUG-COCK  FOG  CHAMBER. 

1.  Introduction. — In  the  last  few  years  I  have  had  occasion  to  use  the 
fog  chamber  extensively  for  the  estimation  of  the  number  of  colloidal* 
nuclei  and  of  ions  in  dust-free  air  under  a  great  variety  of  conditions. 
These  data  were  computed  from  the  angular  diameter  of  the  coronas 
of  cloudy  condensation;    and  it  is  therefore  necessary  to  reduce  all 
manipulations  to  the  greatest  simplicity  and  to  precipitate  the  fog  in  a 
capacious  vessel,  at  least  18  inches  long  and  6  inches  in  diameter.     To 
obtain  sufficiently  rapid  exhaustions  it  is  thus  advisable  to  employ  a 
large  vacuum  chamber,  and  the  one  used  was  about  5  feet  high  and  i 
foot  in  diameter.    The  two  vessels  were  connected  by  18  inches  of  brass 
piping,  the  bore  of  which  in  successive  experiments  was  increased  as  far 
as  4  inches;  but  2 -inch  piping,  provided  with  a  2. 5 -inch  plug  stopcock, 
sufficed  to  produce  all  the  measurable  coronas  as  far  as  the  large  green- 
blue-purple  type,  the  largest  of  the  useful  coronas  producible  in  a  fog 
chamber  by  any  means  whatever.     Moreover,  it  is  merely  necessary  to 
open  the  stopcock  as  rapidly  as  possible  by  hand,  using  easily  devised 
annular  oil  troughs  at  top  and  bottom  of  the  plug,  both  to  eliminate 
all  possible  ingress  of  room  air  and  to  reduce  friction.     Fog  chambers 
larger  than  the  one  measured  were  often  used,  and  it  is  curious  to  note 
that  the  efficiency  of  such  chambers  breaks  down  abruptly,  while  up 
to  this  point  different  apparatus  behaves  nearly   alike.    The  vacuum 
chamber  is  put  in  connection  with  an  air-pump,  the  fog  chamber  with  a 
well-packed  filter  by  the  aid  of  stopcocks.    Water  nuclei  are  precipitated 
between  exhaustions  from  the  partially  exhausted  fog  chamber. 

2.  The  variables. — After  reading  the  initial  pressures  of  the  fog  and 
vacuum  chambers,  it  is  expedient  to  open  the  stopcock  quickly  and 
thereafter  to  close  it  at  once  before  proceeding  to  the  measurement 
of  the  coronas.     Eventually,  i.  e.,  when  the  temperature  is  the  same  in 
both  the  fog  and  vacuum  chambers,  they  must  again  be  put  in  com- 
munication and  the  pressures  noted,  if  the  details  of  the  experiment 
are  to  be  computed. 

*See  Smithsonian  Contributions  No.  1309,  1901;  No.  1373,  1903;  No.  1651,  1906; 
Carnegie  Institution  of  Washington  Publications  No.  40,  1906;  No.  62,  1907.  In  place 
of  the  term  "colloidal  nuclei,"  the  term  "vapor  nuclei"  will  be  used  in  preference  in  the 
text  below.  These  vapor  nuclei  of  dust-free  wet  air  are  probably  aggregates  (physical 
or  chemical)  of  water  molecules. 

i 


2    CONDENSATION  OF  VAPOR  AS  INDUCED  BY  NUCLEI  AND  IONS. 

The  series  of  variables  given  in  table  i,  where  p  denotes  pressure, 
p  density,  r  absolute  temperature,  n  vapor  pressure,  is  to  be  considered. 
The  ratio  of  volumes  of  the  fog  and  vacuum  chambers  was  about 


TABLE  i.  —  Notation.     Drop  of  pressure  dp  =  p-p3,  observed;    dp  =  p-p2,  computed. 


St^e              Fog  chamber. 

i 

Vacuum  chamber. 

Remarks. 

i  i     p 

p 

T 

7t 

P' 

P' 

r 

71 

Initial  states;  cham- 

r 

bers  separated. 

2 

Pi 

Pi 

T! 

X 

P\ 

P'l 

T', 

n\ 

Adiabatic  states, 

after   exhaustion; 

chambers  commu- 

nicating. 

7 

Pi 

Pi 

T! 

TTj 

P*i 

P'l 

^i 

77, 

The  same,  after  con- 

densation of  water 

in  fog  chamber. 

4 

P, 

Pz 

T 

1C 

P'2 

P'Z 

" 

71 

Chambers  separated 
before     condensa- 

tion ensued  ;  orig- 

inal   temperature 

regained. 

5        £ 

P2 

T 

~ 

PT2 

P7! 

T 

71 

Chambers  separated 

after       condensa- 

tion ;  original  tem- 

perature regained. 

6 

Ps 

P3 

T 

7C 

P* 

P& 

T 

n 

Chambers  communi- 

cating   after    ex- 

haustion; original 

temperature      re- 

stored. 

i 

At  the  beginning  (case  i),  the  fog  chamber  is  at  atmospheric  pressure 
p  (nearly),  the  vacuum  chamber  at  the  low  pressure  p1 ',  and  both  at 
the  absolute  temperature  r.  On  suddenly  opening  the  stopcock  the 
adiabatic  pressures,  etc.,  given  under  No.  2  appear,  supposing  that  no 
condensation  has  yet  taken  place  in  the  fog  chamber.  If  the  stopcock 
could  now  be  suddenly  closed  and  the  whole  apparatus  allowed  to 
regain  the  original  temperature  T,  the  conditions  under  No.  4  would 
obtain.  This  is  virtually  the  case  in  Wilson's*  piston  apparatus, 
and  consequently  these  variables  are  comparable  with  his  results 
(cf.  sections  3  and  4).  In  my  apparatus,  however,  condensation  takes 
place  within  the  fog  chamber  before  the  stopcock  can  be  closed,  and 
thus  an  additional  quantity  of  air  is  discharged  from  the  fog  chamber 
into  the  vacuum  chamber.  After  condensation  and  before  the  stopcock 
is  closed  the  conditions  under  No.  3  apply;  when  the  stopcock  has  been 
closed  and  the  apparatus  allowed  to  regain  the  room  temperature  r, 
the  conditions  are  shown  in  No.  5,  and  may  be  observed  with  crude 

*C.  T.  R.  Wilson:  Phil.  Trans.,  London,  vol.  1992,  1889,  pp.  405  et  seq. 


EFFICIENCY    OF    PLUG-COCK    FOG    CHAMBER.  3 

approximation  in  the  isolated  chamber.  Finally,  when  the  chambers 
are  put  in  communication,  the  variables  (No.  6)  are  the  same  in  both. 
This  account  of  the  phenomena  may  seem  prolix,  but  it  is  essential 
to  a  just  appreciation  of  the  efficiency  of  the  plug-cock  fog  chamber. 
Quantities  in  table  i  referring  to  a  given  chamber  may  be  connected  at 
a  given  time  by  Boyle's  law,  as  for  instance,  (p  —  n)=Rp-c.  This  gives 
eleven  equations,  some  of  which  may  be  simplified.  Corresponding 
quantities  in  groups  i  and  2,  as,  for  instance,  r/r1,  may  be  connected 
by  the  law  for  adiabatic  expansion,  giving  two  equations.  In  addition 
to  this,  an  equation  stating  that  a  given  mass  of  air  is  distributed  in  fog 
and  vacuum  chambers  (volumes  v  and  V,  respectively)  is  available;  or 


All  the  quantities  n  are  supposed  to  be  given  by  the  corresponding  T, 
though  at  high  exhaustions  the  lower  limit  of  known  data,  TT  =  /(T),  is 
often  exceeded,  at  least  in  case  of  vapors  other  than  water  vapor. 

3.  Approximate  computation  of  pt  and  p2.  —  It  will  first  be  necessary 
to  compute  p2,  the  pressure  which  would  be  found  in  the  fog  chamber 
when  it  has  again  reached  room  temperature  r,  if  there  were  no  further 
transfer  of  air  from  fog  chamber  to  vacuum  chamber,  due  to  the  con- 
densation of  water  vapor  in  the  former  after  adiabatic  cooling. 

For  the  purpose  of  obtaining  more  nearly  symmetric  equations  it 
seemed  to  be  expedient  to  write 

*lk     and     r/r\ 

at  the  outset,  in  correspondence  with  Boyle's  law,  and  thereafter  to 
correct  for  the  temporary  introduction  of  n  into  the  adiabatic  equation. 
Believing  that  the  completed  equations  would  be  much  more  com- 
plicated by  contrast  than  they  actually  are,  I  made  many  of  the  com- 
putations, where  a  mere  guidance  as  to  the  conditions  involved  is  aimed 
at,  with  these  symmetrical  equations.  The  constants  for  use  will  be 
computed  by  the  more  rigorous  forms  of  sections  4,  5,  8,  and  9.  Mean- 
while the  comparison  of  both  groups  of  equations  will  make  it  easier  to 
pass  from  the  equations  with  p  —  n,  wherever  they  were  used  in  my 
work,  to  the  correct  forms  of  the  next  paragraph.  It  is  for  this  reason 
that  the  equations  now  to  be  given  were  retained. 

The  pressure  p2  is  given  by  the  gages  of  the  piston  apparatus,  since 
there  is  but  a  single  chamber,  and  in  this  respect  the  plug-cock  appara- 
tus differs  from  it  because  the  corresponding  gage-reading  is  essentially 
even  less  than  p2.  (Sections  5  and  9.) 

The  solution  when  the  air  in  both  chambers  is  continually  saturated 
leads  to  transcendental  equations  for  the  adiabatic  pressures  pi=p'i, 


4          CONDENSATION    OF    VAPOR    AS    INDUCED    BY    NUCLEI     AND    IONS. 

which  can  therefore  only  be  obtained  approximately.      If  the  vapor 
pressures  ^  and  n\  correspond  to  p^  and  p\,  the  results  would  be 

,    cjk== 
Pl~~  ~~~- 


-x)  (i+v/V) 


,  _  _.  \c/k 


where  approximate  values  must  be  entered  for  nlt  n\,  plt  in  the  denom 
inator  on  the  right  side  of  the  equation. 
Similarly 


-         (*-e)/* 


Making  use  of  the  values  found  incidentally  elsewhere,  the  data  of 
table  2  were  computed  on  a  single  approximation.  They  are  repro- 
duced in  the  graph  (fig.  i). 

TABLE  2.  —  Successive  values  of  pressure  and  temperature  in  the  plug-cock  fog  cham- 
ber. Volume  ratio  of  fog  and  vacuum  chambers,  v/  F  =  0.064;  P~76',  t=2O°C.\ 
7r=i.7  cm.;  t  refers  to  degrees  C.,  T  to  absolute  temperature,  dp  denotes  the 
drop  in  pressure.  r/r1=(p/pl)l-c/k  and  T/T'I)<=(/>//>/I)I-C/&  assumed. 


Observed.1 

Computed.2 

P. 

/V 

/V 

/>',- 

Pi- 

P\. 

/V 

V* 

P2. 

43-5 
5i-5 
59-5 

45-5 
52-5 
59-7 

47-9 
54-3 

?62.2 

45-6 

46.1 
52.5 
59-3 

46.! 
52.5 
59-3 

54-7 
59-6 
64.6 

44-9 
52.0 

59-4 

49-9 

55-5 
61.5 

«,. 

*v 

ffj. 

^ 

^. 

t\. 

*P*- 

p-ps- 

9P*~ 

P-P2- 

*P»/9P* 

o.o 

.  2 

•  5 

2.2 
1-9 

i-7 

0.7 

•  9 
i.i 

o 

-17.8 
-  8.3 

+      .8 

0 

+    5-2 

9-4 
12.7 

0 

+  24.1 

21.3 
19.8 

0.0 

16.3 

23-5 
30-5 

0.0 

11.4 
16.4 

21.3 

[lo.7o 
J     0.69 

1  These  observat[ons  merely  illustrate  the  equations.     No  attempt  made  at  accuracy.      See  chart. 
s  The  values  of  Pi/Pi  =  0.91,  0.93,  0.95,  respectively. 

The  corrections,  (p2 — p3)  varying  with  (p — pa),  lie  on  a  curve  which 
passes  through  zero,  but  with  a  larger  slope  than  for  dry  air.  In  fact, 
they  are  much  in  excess  of  these  cases*  and  throw  the  whole  phenom- 
enon into  a  lower  region  of  pressures. 

*Am.  Journ.  Science,  xxn,  p.  342,  .1906. 


EFFICIENCY    OF    PLUG-COCK    FOG    CHAMBER. 


*Q*  45*  25° 


FIG.  i. — Pressures  in  plug-cock  fog  and  vacuum  chambers,  for  different  initial  pressures 
of  latter,  the  former  being  initially  at  atmospheric  pressure.  (See  table  i.)  The 
notched  curve  shows  the  march  of  successive  pressures  for  £'  =  45  cm.  and  p  =  6j 
cm.  in  a  single  exhaustion.  The  upper  curves  show  corresponding  temperatures  in 
the  fog  and  vacuum  chambers  under  like  conditions.  The  adiabatic  temperature 
ratio  T/TJ  is  here  an  approximation. 

A  few  incidental  results  deserve  brief  mention.  The  first  of  these  is 
the  nearly  constant  difference  of  about  dp2  =  2  cm.  between  the  observed 
value  p2  (nominal)  and  p3.  Since  for  dry  air  or  not 

(p'2-x)  +v/V  •  (/v-*)  =  (/Y-*)   0  +V/VJ 

is  constant  for  a  given  exhaustion,  dp'2  = — v/V  -  op2.  Hence  if 
dp2  =  2  cm.,  since  v/V  =  0.064,  — dp'2  =  o .064X2  =o .13  cm.,  nearly. 
This  case  is  illustrated  graphically  for  pf  =  45  cm.  in  the  notched  curves 
of  the  figure  in  a  way  easily  understood.  It  seems  probable  that  whereas 
the  smaller  fog  chamber  has  lost  too  much  air  to  even  approach  the 
isothermal  pressures  p2,  the  large  vacuum  chamber  is  only  a  millimeter 
short  of  them  when  the  cock  is  again  closed.  The  constancy  of  the 
observed  difference  p2 — p3  seemed  at  first  to  be  referable  to  the  system- 


6    CONDENSATION  OF  VAPOR  AS  INDUCED  BY  NUCLEI  AND  IONS. 

atic  method  of  investigation,  though  the  effect  of  the  precipitated 
moisture  (which  has  not  yet  been  considered)  will  largely  account  for  it. 
(See  section  9.) 

Anomalous  relations  in  the  data  for  the  fog  chamber,  as  in  the  case 
of  ^'  =  59.5  cm.,  are  direct  errors  of  observation.  On  the  other  hand, 
however,  since  within  the  ranges  of  observation  p  =  a,  P2  =  a2  +  b2p', 
Pz =  aa  +  b3p'  very  nearly,  it  follows  that  (p — p2) / (p — p3)  may  approxi- 
mately be  written  A+Bp',  where  a,  6,  A,  B,  etc.,  are  constant.  Fre- 
quently B  is  negligible,  so  that  (p2 — ps)/(p — p3)  is  constant,  in  which 
case  the  graphs  for  p2 — p3  varying  with  p — p3  pass  through  the  origin. 

4.  Definite  computation  of  p1  and  p2. — If  the  adiabatic  equations  be 
written  without  approximation 

T          j  f     i  + 

and 


TI 

the  equations  for  pl  and  p2  become 


- 


and 


Pt-xJ     V 

from  which  pl  may  be  found  after  putting  an  approximate  form  for  pl 
(p3  nearly)  into  the  vapor-pressure  term  of  the  second  member.     A 
single  approximation  usually  suffices. 
From  these  equations 


follow  at  once.     Subsidiary  equations 


and 


s  , 

remain  as  before  in  section  3.  To  compute  v/V  in  this  way  high  ex- 
haustion is  essential,  otherwise  p'  and  p3  differ  but  slightly.  Between 
the  present  group  of  equations,  which  are  nearly  rigorous,  and  the 
preceding  group  the  corrections  to  be  added  to  the  former  may  be 
estimated. 


EFFICIENCY    OF    PLUG-COCK    FOG    CHAMBER. 


7 


5.  Computation   of  vt/v. — Since    (v1/v)k/c  =  p/pl,  the  volume  expan- 
sion is  a  cumbersome  datum  to  compute  rigorously,  and  it  appears  as 


—  7t 


where  an  approximate  value  of  pl  (nearly  ps,  observed)  must  be  placed 


60 


FIG.  2. — Same  as  fig.  i,  if  the  temperature  ratio  is  corrected 
and  reads  T/TI==(/>//>I)I~C/A; 

in  the  vapor-pressure  terms  of  the  second  member.  For  distinction  [v/  V] 
here  denotes  the  volume  ratio  of  fog  and  vacuum  chambers.  The  terms 
involving  vapor  pressure  may  often  be  neglected,  whereupon  the  equation 


vf     p 


/(l-c/fc) 


+v/V*p 


P_y* 

pj 

reappears,  if  the  equivalent  of  pt  be  inserted.     In  these  cases  pl  may 
again  be  replaced  by  p3. 


8         CONDENSATION    OF    VAPOR    AS     INDUCED    BY    NUCLEI     AND    IONS. 


The  data  for  ply  etc.,  are  given  in  table  3,  and  are  shown  in  the  graphs 
of  fig.  2,  whence  their  differences  from  fig.  i  may  be  ascertained.  The 
respective  pressures  holding  for  ^'  =  45  cm.  are  also  shown  in  a  notched 
curve  and  will  be  further  elucidated.  The  ratio  dp2/dp3  of  the  isothermal 
and  adiabatic  drop  is  here  (table  3)  about  0.68,  or  of  the  same  order  as 
in  table  2. 

TABLE  3. — Definite  computations  corresponding  to  table  2.     p~j6  cm.;   t=2O°; 
7r=i.7;    r/Tl='(p/pl)1-c/ki  and  r/Trl=(p/p'iy-e'k  assumed. 


*,. 

*v 

«, 

P'- 

/>, 

P,           t, 

r, 

P, 

P'z- 

v*. 

Pi/P- 

O.  I 

2-4 

0.6 

43-5 

45-5 

0 

46.4    —  19.0 

25.6 

55-1 

44-9 

1.416 

0.920 

.2 

2.O 

•  Q 

52-5 

52.6  -  9.6 

21.9 

60.  i 

52.1 

1.292 

•939 

•5 

i.7 

i.i 

59-5 

59-7 

59-3    -      -2 

19.8 

64.9 

59-3 

1.181 

•958 

T,. 

P* 

Pi- 

I0x. 

•* 

W, 

^3-Or-Kx) 

P-P2. 

^3  = 

P-P» 

Ratios 

dp2/dpa. 

/>-^ 

4-9 

50.8 

47.2 

5-6 

30-5 

0.401 

0.389 

0.0 

0.0 

1 

9.0 

56.6 

53-5 

4-7 

23-5 

•309 

.297 

ii  .  i 

16.3 

10.677 

12.7 

62.3 

60.  i 

3-6 

16.3 

.214 

.203 

15-9 

23-5 

J        .690 

20.9 

30-5 

J 

6.  Approximate  computation  of  TX. — To  find  the  temperature  of 
the  fog  chamber  after  the  adiabatic  temperature  rl  has  been  raised  by 
condensation  of  fog  to  rly  it  is  apparently  necessary  to  compute  p2 
first,  and  then  proceed  by  the  method  used  by  Wilson*  and  Thomson. 
When  the  vacuum  chamber  is  large,  however,  its  pressures  vary  but 
slightly,  and  therefore  the  pressure  observed  at  the  vacuum  chamber 
after  exhaustion,  p3,  when  the  two  chambers  are  in  communication,  is 
very  nearly  the  adiabatic  pressure  of  the  fog  chamber,  pv  This  result 
makes  it  easier  to  compute  not  only  TI}  but  incidentally  the  water,  m, 
precipitated  per  cubic  centimeter  (without  stopping  to  compute  the 
other  pressures),  with  a  degree  of  accuracy  more  than  sufficient  when 
the  other  measurements  depend  on  the  size  of  coronas. 

To  show  this,  let  d,  L,  and  n  refer  to  the  density,  latent  heat  of 
vaporization,  and  pressure  of  water  (or  other)  vapor;  let  p,  k,  c,  T, 
denote  density,  specific  heat  at  constant  pressure,  specific  heat  at  con- 
stant volume,  and  absolute  temperature  of  the  air,  the  water  vapor 
contained  being  disregarded  apart  from  the  occurrence  of  condensation. 
As  above  let  the  variables,  if  primed,  belong  to  the  vacuum  chamber, 
otherwise  to  the  fog  chamber.  Let  the  subscripts,  etc.,  also  be  similarly 
interpreted,  so  that  d  is  the  known  density  of  saturated  water  vapor  at 
T°  absolute. 

*C.  T.  R.  Wilson:    Phil.  Trans.,  London,  vol.  189,  p.  298,  1897. 


EFFICIENCY    OF    PLUG-COCK    FOG    CHAMBER.  9 

Assuming  the  law  of  adiabatic  expansion  to  hold  both  for  gaseous 
water  vapor  and  for  wet  air  in  the  absence  of  condensation,  it  is  con- 
venient in  a  plug-cock  apparatus  of  fog  and  vacuum  chamber  (where 
pi  is  nearly  given  by  pa)  to  reduce  to  adiabatic  conditions;  whence 


where  m  is  the  quantity  of  water  precipitated  per  cubic  centimeter  of 
the  exhausted  fog  chamber.  Finally  d,  the  density  of  saturated  water 
vapor,  must  be  known  as  far  as  r,  so  that  an  equation  d—f(r)  is  addition- 
ally given.  Here  7it  the  vapor  pressure  at  rlt  is  usually  negligible  (about 
0.5  cm.)  as  compared  with  plt  and  pt  may  in  practice  (where  great 
accuracy  is  not  demanded)  be  replaced  by  p3,  which  like  p  is  read  off, 
while  TT  holds  at  T,  which  is  also  read  off.  In  the  next  section  I 
give  a  numerical  example,  taken  from  table  2,  for  £'  =  43.5  cm. 

If  the  original  equation  (isothermal)  is  taken,  m  =  $.  36X10  ~6  grams 
per  cubic  centimeter.  If  the  above  equation  is  taken,  w  =  5  .  35X  io~~6. 
If  the  same  equation  is  taken  and  p1  replaced  by  p3,  m  =  $  -3oX  io~6, 
the  error  being  i  per  cent  of  the  true  value,  which  is  near  enough  in 
practice  or  admits  of  easy  correction. 

7.  Approximate  computation  of  p2.  —  Since  the  plug  stopcock  can 
not  be  closed  before  the  water  condenses  in  the  fog  chamber  after 
sudden  exhaustion,  the  pressure  observed  in  the  fog  chamber  when  the 
room  temperature  reappears  is  smaller  than  p2.  An  excess  of  air  has 
passed  to  the  vacuum  chamber,  so  that  the  pressure  within  the  fog 
chamber  is  eventually  p2,  or  less.  The  equation  for  pl  and  p\  remains 
as  in  section  3,  or  better,  as  in  section  4. 

The  new  quantities  are 


ri 

where  pl  is  the  density  of  air  at  rt.    The  ratio  pj  pv  may  be  found  when 
T  is  known  as 


Pi  (Pi—Kj  (TI/ 

where  r\  and  T^,  n\  and  n\,  pl  and  p\  are  nearly  the  same.     The  last 
equation  may  usually  be  written 


10     CONDENSATION    OF     VAPOR    AS     INDUCED    BY    NUCLEI     AND    IONS. 


and  the  small  quantity  involving  the  vapor  pressures  n  treated  as  a 
correction.  It  amounts  to  about  i  per  cent  of  the  large  quantity.  The 
values  of  p2  are  also  given  in  the  table  and  chart.  This  shows  that  p2 
observed  is  always  smaller  than  p2  computed,  even  when  allowance 
is  made  for  the  condensation  of  water;  i.  e.,  the  fog  chamber  begins  to 
appreciably  heat  itself  above  the  temperature  TI  before  the  cock  can  be 
closed  again,  so  that  when  isolated  it  contains  less  than  its  proper 
quantity  of  air.  Only  the  initial  and  the  final  (both  chambers  com- 
municating) pressures  may  therefore  be  taken  at  the  fog  chamber. 
(Cf.  section  9.) 

8.  Rate  of  reheating  of  fog  chamber. — There  is  a  final  question 
at  issue,  relating  to  the  rate  at  which  heat  flows  into  the  adiabatically 
cooled  fog  chamber.  Experiments  may  be  made  by  opening  the  exhaust 
cock  for  stated  lengths  of  time  t.  The  vacuum  pressure  being  pf  =  48 . 6, 
the  datum  for  t  =  o  second  may  be  computed  as  ^2  =  57.8  cm.,  or  after 
condensation  ^  =  52.4  cm.  Table  4  contains  the  results,  and  they  are 
fully  mapped  out  in  chart,  fig.  3.  The  notched  curves  show  the  suc- 
cessions of  pressure  in  both  chambers.  Neither  p2  nor  p'2  may  be  ob- 
served, since  the  chambers  communicate  during  the  opening  of  the  stop- 
cock for  a  period  certainly  longer  than  o .  i  second.  Observable  pressures 
are  shown  on  the  vertical  line  below  p2  and  above  p'2.  Hence  within 
a  quarter  of  a  second  the  final  isothermal  pressure  (/  =  oo ,  chambers 
communicating)  is  already  regained  to  more  than  60  per  cent,  and  this  in 
spite  of  the  fact  that  the  capacity  of  the  fog  chamber  is  over  6  liters. 
Hence  the  attempt  to  observe  p2  (isothermal  temperature  after  con- 
densation) at  the  fog  chamber  is  idle.  It  practically  reaches  p3  if  the 
exhaust  cock  is  open  about  10  seconds.  The  pressure  p2  is  never  reached, 
yet  p2  is  exceeded,  owing  to  the  counteraction  of  the  vacuum  chamber. 
Finally  p±  may  be  virtually  read  off  in  case  of  a  large  vacuum  chamber 
by  adding  a  slight  correction  for  p3.  This  is  one  of  the  advantages  of  the 
method. 

TABLE  4. — Rate  of  heat  influx.     Barometer,  76.0  cm. 


t. 

£'• 

l*V 

Observed 
P* 

P'3- 

P* 

sec. 

cm. 

cm. 

cm. 

cm. 

cm. 

0.25 

48.6 

50.2 

53-2 

50-3 

50.6 

i 

48.6 

50.2 

52.0 

50.2 

50.5 

2-5 

48.6 

50.4 

51-5 

50.4 

50.5 

5 

48.6 

50.2 

50-9 

50.2 

50.3 

•  5 

48.6 

50.2 

52.7 

50.2 

50.2 

From    chart  £'  =  48.6;    £3=57.8;    £2=52.4  cm, 
'Ftom  the  chart  />/1  =  5o.2;    £'3=50.0. 


EFFICIENCY    OF    PLUG-COCK    FOG    CHAMBER. 


II 


O*'          / 


FIG.  3. — Observed  value  of  apparent  isothermal  pressure  p2,  after  lapse  of  different 
seconds  of  time  after  exhaustion;  also  corresponding  drop  of  pressure  df>2  from 
atmospheric  pressure. 

9.  Definite  computation   of    rlt    pt,    r2,    p2,    etc. —  In    view    of    the 

equation 


the  density  of  saturated  vapor  at  the  temperature  r  becomes 

"c/*      c      - 


where  d  is  the  density  of  saturated  water  vapor  at  T;  p,  c,  L,  the  density 
of  air,  its  specific  heat  at  constant  volume,  and  its  latent  heat.  The 
other  quantities  have  the  same  meaning  as  before.  Hence  the  quantity 


12     CONDENSATION    OF    VAPOR  AS    INDUCED    BY    NUCLEI    AND    IONS. 

of  water  precipitated  per  cubic  centimeter  of  the  exhausted  fog  cham- 
ber is 


If  the  coefficient  of  d  in  the  above  equations  be  written  x, 


where  a  and  b  are  constant,  so  that  r  is  the  temperature  at  which  the 
line  J,  T,  crosses  the  vapor-pressure  curve  d  =  f  (rj,  which  for  water 
vapor  is  known  as  far  as  —  50°  C.  In  place  of  absolute  temperatures  r, 
degrees  centigrade  ^  and  ^  may  be  used.  Table  5  contains  a  series  of 
useful  data  for  m,  dp  (if  £  =  76),  dp/p,  v1/v,  /lf  and  /r 

TABL,E  5.  —  Water   precipitated  at  different  exhaustions   and   temperatures. 
£  =  76  cm.;  dp3=p  —  p3cm. 


a 

•y 

dp 
P 

dp. 

At  10°  C. 

At  20°  C. 

At  30°  C. 

wXio6. 

<i- 

t 

wXio6. 

*l- 

'l- 

wXio8. 

*l. 

*i- 

i.  ii 
1.24 
i-43 
1.56 
2.15 

0.132 
.263 
•395 
.466 
.660 

IO 

20 

30 
40 
50 

1.88 
3-4i 
4.48 

-    i-4 
—  14.0 

-28.4 

+   4.6 

-    1.8 

—  IO.O 

2.  26 
4.l8 
5.65 

6.61 

7-58 

+  8.3 

-  4-8 
-19.7 
-37-1 
-58-3 

+  15.9 

+  10.9 

+  4-6 
-  3-3 
-  9-5 

2.61 
4.91 
6-75 

+  17.8 

+   4-3 
—  ii  .  i 

26.6 
22.7 
17.8 

Incidental  data,  dp  =  p  —  p1. 

1.18 

1.29 
1.42 

o.  214 

•309 
.401 

16.3 
23-5 
30.5 

3.57     -19.0 
4-75     ~   9-6 

5.58      -        .2 

+  12.7 
+  9.0 
+  4-9 

.... 

To  compute  p2  and  p\  the  equations  are 

,1-c/fc 

and     £'o- 


i-c/k 


where  pj  pv  depending  upon  Boyle's  law,  will  have  the  same  value  as 
before  (section  7)  and  in  the  approximate  form  becomes 


Since 


i  —  7T        T* 


with  a  similar  equation  for  //lf  the  pressures  p±  and  />/1  may  be  computed, 
since  the  values  of  the  second  member  of  the  equation  are  now  known. 


EFFICIENCY    OF    PLUG-COCK    FOG    CHAMBER.  13 

10.  Conclusion. — If  the  fog  chamber  is  combined  with  a  large 
vacuum  chamber,  through  a  sufficiently  wide  passageway  containing  an 
ordinary  plug  gas-cock  to  be  opened  and  closed  rapidly  by  the  hand,  all 
the  measurable  coronas  of  cloudy  condensation,  due  to  the  presence  of 
colloidal  or  vapor  nuclei  in  wet,  strictly  dust-free  air,  may  be  evoked. 
While  such  an  apparatus  admits  of  capacious  fog  chambers  and  ex- 
tremely simple  manipulation,  it  has  not  been  shown  to  be  inferior  in 
efficiency  to  any  other  apparatus  whatever. 

The  conditions  of  exhaustion  must,  however,  be  computed  from  the 
initial  pressures  of  the  fog  and  vacuum  chambers  when  separated  and 
their  final  pressure  (after  exhaustion)  when  in  communication,  in  all 
cases  at  the  same  temperature  and  the  volume  ratio  of  the  chambers. 
The  chief  pressures  and  temperatures  are  shown  in  fig.  2  for  different 
initial  pressures  of  the  vacuum  chamber,  the  fog  chamber  being  at 
atmospheric  pressure. 


CHAPTER    II. 

THE  CHANGE  OF  THE  VAPOR  NUCLEATION  OF  DUST-FREE  WET  AIR  IN 
THE  LAPSE  OF  TIME,  TOGETHER  WITH  THE  EFFECT  OF  THE  LIMITS 
OF  PRESSURE  BETWEEN  WHICH  A  GIVEN  DROP  TAKES  PLACE  ON 
THE  EFFICIENCY  OF  THE  FOG  CHAMBER. 

11.  Introduction. — Recently*  I  published  certain  results  which  showed 
(apparently)  that  the  colloidal  nucleation  of  dust-free  air  varies  peri- 
odically in  the  lapse  of  time  in  a  way  closely  following  the  fluctuations 
of  the  barometer.  This  nucleation  (particularly  when  the  larger  groups 
of  nuclei  lying  near  the  region  of  ions  are  taken  into  consideration)  is  a 
maximum  when  the  barometer  is  a  minimum.  The  development  of 
the  investigation  was  peculiar.  At  the  outset  the  data  appeared  like 
an  immediate  confirmation  of  Wood  and  Campbell'sf  discovery,  which 
had  then  just  been  announced.  Maxima  of  colloidal  nucleation  appeared 
where  Wood  and  Campbell  had  found  minima  of  ionization,  and  vice  versa. 
By  supposing  that  the  ions,  which  are  virtually  larger  than  the  colloidal 
nuclei,  capture  most  of  the  precipitated  water,  the  two  sets  of  results 
would  be  mutually  corroborative. 

Later  this  cosmical  feature  of  the  phenomenon  became  of  secondary 
importance  as  compared  with  an  apparent  direct  effect  of  fluctuations 
of  the  barometer.  Nucleation  of  dust-free  air  increased  when  the  barom- 
eter decreased,  and  maxima  of  nucleation  were  apt  to  coincide  with 
minima  of  the  barometer.  Such  a  result,  whether  direct  or  indirect 
(removal  of  radioactive  matter  from  porous  earth  accompanied  by 
falling  barometer),  would  have  been  of  considerable  importance,  and 
great  care  had  to  be  taken  in  the  endeavor  to  verify  it.  Unfortunately 
the  correction  to  be  applied  for  barometer  fluctuation,  in  its  effect  upon 
the  aperture  of  the  coronas,  was  in  the  same  sense  and  very  difficult  to 
estimate;  and  in  fact  upon  using  two  fog  chambers  side  by  side  (one 
with  2 -inch,  the  other  with  4-inch  exhaust  pipes),  adjusted  for  different 
sizes  of  coronas  and  accentuating  the  barometric  correction,  the  vari- 
ations in  one  vessel  might  be  made  to  show  a  tendency  to  follow  the 
barometer,  whereas  the  other  departed  from  it.  Table  6  and  fig.  4  give 
an  example  of  such  a  case,  where  dp  is  the  observed  fall  of  pressure 
(P~p3)>  P  the  pressure  of  the  fog  chamber  before,  p3  the  pressure  after 

*Carnegie  Institution  of  Washington  Publication  No.  62,  chap,  vi,  1907.  Cf.  Science, 
xxm,  p.  952,  1906;  xxiv,  p.  180,  1906. 

fWood  and  Campbell:    Nature,  LXXIII,  p.  583,  1906. 
14 


CHANGE  OF  VAPOR  NUCLEATION  IN  LAPSE  OF  TIME. 


exhaustion  with  fog  and  vacuum  chamber  in  communication,  all  at  the 
same  temperature;  5  is  the  angular  diameter  of  the  corona  on  a  radius 
of  30  cm.,  when  the  source  of  light  and  the  eye  are  at  30  cm.  and  at 
250  cm.  on  opposite  sides  of  the  fog  chamber.  Finally,  n  shows  the 
number  of  nuclei  per  cubic  centimeter. 

TABLE  6. — Time  variation  of  the  larger  colloidal  nucleation  of  dust-free  air.    Conical 
filter,     dp  readjusted.     App.  I,  4-inch  pipes;   app.  II,  2-inch  pipes. 


Date,  etc. 

Apparatus  I. 

Apparatus  II. 

dp,. 

si- 

P. 

s\. 

n  Xio-3. 

3P» 

S2. 

sz. 

w2Xio~3. 

July  12,       8h50ra 

27.1 

3-9 

76.2 

3-9 

19 

25-5 

2-9 

3-3 

IO 

3  45 

27.2 

5-i 

76.2 

4-9 

37 

25-5 

2.6 

3-o 

7 

5  35 

27.1 

5-2 

76.1 

5-i 

4i 

25-7 

3-2 

3-0 

7 

July  13,      10  40 

27-3 

5-2 

76.1 

4.8 

35 

25-4 

3-i 

3-7           16 

3  oo 

27.1 

5-2 

76.1 

5-i 

4i 

25-4 

2-5 

3-3 

IO 

5  30 

27.2 

5-o 

76.0 

4-7 

33 

25-6 

2-5 

2-4 

3-7 

July  14,       8  41 

27.2 

5-6 

76.0 

5-3 

46 

25-4 

2.6 

2.O 

2.  I 

3  20 

27.2 

5-o 

75-9 

4.6 

30 

25-6 

2-4 

2-3 

3-o 

6  oo 

27.4 

5-7 

75-8 

5-o 

39 

25-7 

3-o 

2.6 

5-2 

July  15,       8  oo 

27-3 

5-2 

75-9 

4-7  |            33 

25-6 

3-o 

7-4 

3  30 

27.2 

5-6 

75-9 

5-2 

43 

25.2  j    2.6 

3-5 

12.7 

5  25 

27.2 

5-2 

75-9 

4.8 

35 

July  1  6,       9  oo 

27-3 

5-5 

75-7 

4-9 

37 

25-5 

2.9 

2.9 

"6.7 

2  30 

27-3 

5-4 

75-7 

4.8 

35 

25-6 

3-i 

2-9 

6.7 

6  oo 

27-5 

6-3 

75-6 

5-4 

49 

25-4 

2.8 

3-o 

7-4 

July  17,       9  oo 

27-3 

5-  7 

75-5 

5-o 

39 

25-7 

3-5 

2.8 

6.2 

4  oo 

27-3 

6.7 

75-3 

5-8 

58 

25-6 

3-2 

2.6 

5-2 

July  18,       9  51 

27.2 

5-5 

75-8 

5-o 

39 

25.2 

2-5 

3-4 

ii.  5 

3  55 

27-3 

5-4 

75-8 

4.8 

35 

25-7 

2.9 

2.4 

3-7 

9  15 

27.4 

5-i 

76.3 

4.6 

30 

25-6 

2.6 

2-4 

3-7 

2  30 

27-3 

5-2 

76.2 

4.8 

35 

25-6 

2.8 

2-7 

5-9 

6  10 

27-4 

6.1 

76.2 

5-6 

54 

25.6 

2.O 

i-9 

2.O 

While  the  data  for  apparatus  I  still  recall  the  barometer  graph,  this 
is  not  the  case  for  apparatus  II,  and  neither  of  the  graphs  I  or  II  are 
as  strikingly  suggestive  of  the  variations  of  atmospheric  pressure  as 
was  the  case  in  the  earlier  report.  The  discrepancy  in  the  new  results 
may  be  an  overcompensation,  although  all  the  details  of  the  experi- 
ments themselves  were  gradually  more  and  more  fully  perfected;  or 
the  rise  in  the  region  of  ions  may  just  balance  the  decrease  of  the  num- 
ber of  efficient  colloidal  nuclei  due  to  the  increase  of  the  former.  In 
fact  the  region  where  ions  predominate  may  rise  while  the  regions  where 
the  vapor  nuclei  are  more  important  may  correspondingly  decrease, 
producing  a  diminished  slope  of  the  initial  part  of  the  graph  such  as  is 
often  actually  observed.  It  is  necessary,  therefore,  to  inquire  somewhat 
more  carefully  into  the  errors  involved,  to  investigate  some  datum  or 
invariant  which  if  kept  constant  will  mean  a  corona  of  fixed  aperture 
in  the  given  apparatus,  unless  there  is  actual  radiation  in  varying 
amount  entering  from  without. 


16          CONDENSATION    OF    VAPOR   AS    INDUCED    BY    NUCLEI    AND    IONS. 


I  purpose,  therefore,  in  the  present  paper,  to  study  the  same  phenom- 
enon for  an  artificial  barometer;  in  other  words,  to  accentuate  the 
present  discrepancies,  let  the  pressure  drop  from  a  given  upper  limit  to 
varying  lower  limits,  as  well  as  from  varying  upper  limits  to  a  given 
lower  limit.  The  results  so  obtained  are  enormously  different  for  the 
same  drop  of  pressure.  Much  of  this  would  be  anticipated;  but  the 
question  nevertheless  arises  whether  the  colloidal  nucleation  of  the  gas 
is  actually  dependent  in  so  marked  a  degree  on  its  initial  pressure,  or 
whether  this  dependence  can  be  explained  away. 
74 


16 


78 


30 


ZO 


to 


cfycvro 


P 


A 


fVeib 


10 


7  July     9  11  13          tJ"          77          13          21 

FIG.  4. — Apparent  nucleation  of  dust-free  air  in  lapse  of  time.  Apparatus  I  with 
4-inch  exhaust  pipes;  apparatus  II  with  2-inch  exhaust  pipes;  otherwise  identical. 
A  new  and  more  pervious  filter  was  installed  on  July  1 1 .  The  upper  curve  shows 
corresponding  barometric  pressure  within  the  fog  chamber. 

Later  in  the  course  of  the  work  I  made  additional  comparisons  with 
the  contemporaneous  ionization  of  the  air  determined  by  Miss  L.  B. 
Joslin  and  with  the  temperature  of  the  fog  chamber  as  distinguished 
from  the  temperature  of  the  air.  These  results  as  a  whole  finally  showed 
that  a  direct  dependence  of  the  vapor  nucleation  of  the  dust-free  air 


DATA  OF  VARYING  PRESSURE.  17 

in  the  fog  chamber  on  the  barometer,  on  the  ionization  of  the  air,  on 
any  form  of  external  radiation,  or  on  the  temperature  of  the  atmosphere, 
can  not  be  detected.  All  the  variations  may  be  referred  to  the  temper- 
ature of  the  fog  chamber  itself,  as  if  it  generates  increasing  numbers  of 
colloidal  nuclei  as  its  temperature  increases.  Since  the  colloidal  nuclei 
in  dust-free  moist  air  are  to  be  associated  (from  my  point  of  view)* 
with  the  saturated  vapor,  and  are  only  secondarily  dependent  upon  the 
air  itself,  the  result  so  obtained  is  curious,  as  one  would  expect  a  decrease 
of  the  colloidal  nucleation  with  rise  of  temperature.  Correction  for  the 
increased  water  precipitated  at  higher  temperatures  merely  accentuates 
the  difference.  If  rl  is  the  low  (absolute)  temperature  obtained  by 
sudden  expansion  adiabatically  from  r  the  ratio  TJ/T  should  be  wholly 
dependent  upon  the  corresponding  pressures;  and  yet,  for  the  same 
ratio,  more  nuclei  are  obtained  as  T  is  larger.  This  difference  of  be- 
havior is  maintained  for  larger  and  smaller  ratios  of  r1/r,  in  like  degree. 

12.  Data. — The  results  are  given  in  tables  7  and  8,  and  refer  to  a 
fog  and  vacuum  chamber,  the  volume  ratio  of  which  is  about  v/V  =  0.06, 
combined  with  sufficiently  wide  piping  (2 -inch  bore)  and  an  interposed 
(2.5-inch)  stopcock.  The  former  communicates  with  the  filter,  the 
latter  with  the  air-pump.  At  the  same  temperature  the  fog  and  vacuum 
chambers  are  initially  (before  exhaustion)  at  pressures  p  and  p',  finally 
at  pressure  p3,  when  in  isothermal  communication  after  exhaustion; 
p2  and  p\,  respectively,  would  be  the  pressures  at  the  given  temperature 
if  the  chambers  could  be  isolated  immediately  after  exhaustion  and 
before  the  precipitation  of  fog.  P  denotes  the  barometric  pressure,  and 
pm  the  initial  gage-reading  within  the  fog  chamber  before  exhaustion, 
so  that  the  drop  of  pressure  is  (apart  from  the  moisture  content,  which 
will  be  treated  in  turn  below)  dp  =  P—pm—p3,  and  the  drop  of  pressure 
takes  place  from  p  =  P—pm  adiabatically  to  plt  isothermally  to  p2  if  the 
fog  chamber  were  isolated  as  specified,  or  isothermally  to  p3  when  fog 
and  vacuum  chambers  are  left  in  communication. 

For  a  given  value  of  P  the  same  drop  of  pressure  dp  may  thus  be 
obtained  in  two  ways — either  by  giving  a  suitable  value  to  pm,  i.  e.,  by 
starting  with  a  partially  exhausted  fog  chamber  and  a  vacuum  chamber 
at  fixed  exhaustion  p' ',  which  implies  a  nearly  fixed  pz\  or  by  keeping 
pm  constant  (small,  nearly  zero),  thus  starting  with  the  fog  chamber 
about  at  atmospheric  pressure,  and  determining  p'  of  the  vacuum 
chamber  and  therefore  p3. 

Briefly,  then,  the  condensational  effects  of  a  given  difference  dp  when 

lying  between  different  pressures  p  and  p3,  are  to  be  tested,  and  this  is 

best  accomplished  by  constructing  separate  complete  graphs  for  the 

aperture  5/30  of  the  coronas,  first  by  keeping  p'  and  p3  nearly  constant 

*Am,  Journ.  Sci.,  xxn,  p.  136,  1906. 


i8 


CONDENSATION    OF   VAPOR   AS    INDUCED    BY    NUCLEI    AND    IONS. 


and  varying  pm  (lower  pressure  limit,  p,  variable)  and  second  by  keeping 
p  fixed  and  varying  p'  and  p3  (upper  pressure  limit  variable).  Tables 
7  and  8  show  these  data,  the  latter  for  a  wider  range  of  coronas  than  the 

v 


FIG.  5. — Nucleation  of  dust-free  air  for  different  drops  of  pressure  dp  =  p  —  p.2;  [dp]' 
denoting  that  the  upper  limit,  [dp^  that  the  lower  limit  of  the  drop  of  pressure  dp 
is  varied.  Also  corresponding  nucleation  referred  to  the  exhaustion  dp/p.  Four 
series.  Small  ranges  of  nucleation  as  compared  with  fig.  6. 

former,  while  n  denotes  the  number  of  nuclei  per   cubic  centimeter. 
From  5  the  number  of  nuclei,  n,  per  cubic  centimeter  is  computed. 

The  results,  moreover,  are  graphically  given  in  figs.  5  and  6,  the  abscis- 
sas being  the  drop  dp=p—p2,  the  ordinates  nX  io~3.  It  will  be  seen  at 
once  that  the  two  curves  ([dp^  denoting  that  the  lower  limit  of  pressure, 


DATA  OF  VARYING  PRESSURE. 


[dp]'  that  the  upper  limit  of  pressure  is  varied)  are  strikingly  distinct  in 
both  figures  and  that  the  variation  of  the  lower  pressure  limit  [dp^ 
corresponds,  as  it  should,  to  a  highly  increased  efficiency  of  the  fog 
chamber.  The  coronal  fog  limits  are  far  apart,  being  respectively  below 
[^]i  =  I7-4  and  [dp]'  =  19  -4  cm.  in  fig.  6,  where  all  data  (table  8)  were 
obtained  in  one  series  of  experiments. 


7.  —  Effect  of  varying  p  in 
P-pm.    v/V  =  o.o64;   p-p 


Chamber  II.    Bar. 


dp;  71=2.3;   ^=25 


P. 

P*. 

*>-/>»• 

#. 

S. 

Cor. 

ttXio-3. 

dp/p. 

P- 

I  

7C    7 

1O    2 

27     7 

27    I 

6   Q 

2'  B  P 

2io5 

O.  ^SQ 

7C    c 

.  I 
I  .O 
2  .O 

•  5 
•  5 

.  -2 

•4 
26.5 

2S  .  ^ 

6.9 

7.0 

S  .  I 

g'BP 
g'B  P 

2io6 
104 

7Q 

.362 
.355 

•  344 

75-6 
71.7 

77.7 

II 

7tr    7 

2.O 

3-o 
3-o 

4.0 
4.0 

6.0 

30    I 

.6 
.6 

•  7 
.8 

•  7 
.6 

27    6 

25.6 
24.6 
24-7 
23-8 
23-7 

21.6 

27    S 

6.4 

4-5 
4.2 

2-5 
2.4 

i-5 
Q.  S 

w  y 
w  r 

72 
27 
21 

4-3 
3-5 
1.4 

190 

.348 
•339 
•340 
•332 
•331 
•311 

.364 

73-7 
72.7 
72.7 
71.7 
71.7 
69.7 

75.6 

4.0 

I.O 

6  o 

!e 

.8 

23-7 
26.6 
21.8 

2.4 

7-i 
1.8 

g'BP 

3-9 
116 
1.6 

•331 
•356 
.313 

71.7 

74-7 
69.7 

I'  

7C    c 

I.O 
O    2 

.6 

24..  Q 

26.6 

24.  7 

7-5 
i  .  7 

g'BP 

116 

1.8 

.356 
.328 

74-7 
75-3 

t  —  21  4°  C 

2^    6 

oc    4. 

-\  6 

1  1; 

.  -IT.J 

JT   —  !     I     Q 

26    4. 

26    2 

5  6 

C7 

•348 

;r-7r1=    1.4. 

IP  

476.2 

.  2 

25.  Q 

2^.  7 

3-  2 

cor 

9-5 

•338 

76.0 

*=23°C. 

7T    =     2.1. 
71  —  71-^=     1.6. 

5I 

7  e     c 

2 

26.9 
27.4 
28.7 
29.4 

30.5 
33-5 

24.    Q 

26.7 
27.2 
28.5 
29.2 

30.3 
33-2 

24.   7 

6.4 

6.8 

10.2 
12 
13? 
13? 

I  .7 

wp 
gB  P 
w  r 
yr 
gBP 
Do 

76 

120 
210 
310 
380 
4IO 

1.8 

.351 
•359 
•375 
.384 

•399 
•437 

.328 

75-3 

4    =  ,2~0p 

2c    6 

2  c    j. 

i  6 

15 

•337 

*      *o   v*. 

^O  •" 

26    A. 

26    2 

^  6 

53 

•348 

7T  —  7T!=      1.6. 

^u"4- 

1  Water  nuclei  not  precipitated.  4  From  Carnegie  Institution    of  Wa.shin^ton 

2  Too  small .     Initial  values.  Publication  No.  62,  chapter  n,  table  26. 

3  Water  nuclei  precipitated.     Coronas  usually  blurred.     5  Ibid.,  chapter  vi,  table  x. 

In  fig.  5  the  results  of  series  lr  and  II'  are  taken  from  data  for  the 
same  apparatus  in  an  earlier  report  to  the  Carnegie  Institution  of  Wash- 
ington.* Consequently  some  reconsideration  is  needed.  In  the  lapse 
of  time  the  efficiency  of  the  fog  chamber  has  for  some  reason  increased, 
for  the  new  results  (fig.  6  and  dotted  line  in  fig.  5)  are  distinctly  higher 
in  nucleation  than  those  quoted  from  the  report. 

*Carnegie  Institution  of  Washington  Publication  No.  62,  chapters  n  and  vi,  1907. 


20 


CONDENSATION    OF   VAPOR   AS    INDUCED    BY    NUCLEI    AND    IONS. 


Compared  with  the  graph  n  and  [dp]',  table  7,  where  the  upper  limit 
only  is  varied,  the  graph  n  and  [dp]±  lies  in  the  main  above  it,  in  the 
smaller  exhaustions,  and  it  should  be  remembered  that  the  range  of 
variation  is  here  smaller.  But  it  does  not  lie  as  much  above  n  and 
[dp]'  throughout  as  would  be  expected,  seeing  that  only  the  upper  points 


FIG.  6.— Nucleation  of  dust-free  air  for  different  drops  of  pressure  dp  =  p  —  pz\  [dp]' 
denoting  that  the  upper  limits,  \dp\  that  the  lower  limit  of  the  drop  of  pressure 
dp  is  varied.  Also  corresponding  curve  referred  to  the  exhaustion  dp/ p.  Three 
series.  Larger  ranges  of  nucleation  than  in  fig.  5. 

should  coincide,  intimating  that  there  is  some  variation  as  compared 
with  fig.  6  not  accounted  for.  This  becomes  specially  evident  when 
the  two  graphs  for  [dp]  in  figs.  5  and  6  are  compared,  as  shown  in  the 
former. 


DATA    OF    VARYING    PRESSURE. 
TABLE  8. — Data1  corresponding  to  table  7  for  larger  ranges  of  dp. 


21 


P. 

£m- 

P-P* 

<?/>  = 
£-#.- 

S. 

Cor. 

nXio~3. 

/>• 

III  

7S   8 

O.  I 

27    6 

27     5 

91 

w  r 

1  7Q 

7  c    7 

7T    =2.5 

/  O  '  *-* 

*•  1    *\J 

28.5 

•*  /  •  3 

28.4 

•  l 

ii.  5 

2w  r  o 

1  /  y 
244 

/  0  •  / 

7T  —  TTj  =  2  .  O 

29.1 

29.0 

n.  8 

2w  r  o 

332 

29.9 

29.8 

g 

375 

26.8 

26.7 

8.0 

139 

25-4 

25-3 

4-3 

24 

26.6 

26.5 

7-3 

H5 

IV.    ... 

7S    8 

.  I 

-IQ     O 

2Q    Q 

fir  v  o 

"^ilO 

7  c    7 

71   =2.5 

/  O  •  u 

1.0 

O"  •  *•* 

30.1 

•*  Z7   "  V 

29.1 

5  J   *-* 

g'o 

OH-*-1 

372 

/  0  •  / 

74-7 

7T  —  7T1  —  2  .  O 

2.0 

30.2 

28.2 

ii 

gyo 

327 

73-7 

3-o 

30.1 

27.1 

ii 

w  r  o 

234 

72.7 

4.0 

30.1 

26.1 

9-5 

w  r 

182 

71.7 

5-o 

30.3 

25-3 

8.6 

w  c 

157 

70.7 

6.0 

30-3 

24-3 

7.0 

w  r 

93 

69.7 

7-o 

30.3 

23-3 

5-4 

44 

68.7 

8.0 

30.3 

22.3 

2.8 

5-7 

67.7 

v 

7q  8 

i 

28  •* 

28.2 

1  1 

y'  r  o 
j.  \j 

24.2 

75    7 

7T    =2.5 

/  0  •  ° 

.  i 

^o  .  ^ 
25-3 

25.2 

2-9 

•*•*•* 

6.6 

/  O  •  / 

7T  —  7Tt  =  2  .  O 

1  Color  distortion.     The  value  of  s  corresponds  to  g  y  at  least. 

2  Fog  chamber  cleaned  of  water  nuclei  after  each  observation. 

13.  Explanation. — It  will  next  be  necessary  to  endeavor  to  coordinate 
the  two  curves  for  [dp]t  and  [dp]'.  If  the  absolute  temperatures  of  the 
air  within  the  fog  chamber  before  and  after  exhaustion  are  r  and  rt 
(adiabatic  pressure  pt)  then  apart  from  the  condensation  of  water  vapor 
at  the  original  vapor  pressure  n  at  r,  we  may  write  as  one  extreme  case, 


With  a  large  vacuum  chamber  the  difference  between  p1  and  p3  is  very 
small  relatively  to  pl  and  p3,  so  that  for  the  present  purposes  p — pd  = 
p — Pi  =  dp  (nearly),  whence 

dp—  (TT—  Trjyfc-c)/* 

P-X       / 
Similarly  we  may  write  as  a  second  extreme  case, 


or  the  degree  of  sudden  cooling  from  a  fixed  temperature  T  to  the  adia- 
batic temperature  rl  depends  primarily  on  dp /p.  This  would  in  any  case 
be  permissible  for  comparison  in  table  6,  where  a  continuous  series  of 
experiments  is  made  at  the  same  temperature.  The  moisture  error  is 
thus  a  constant  throughout.  Hence  the  apertures  of  coronas  s,  and  the 
nucleation  n,  will  be  a  function  of  dp/p  to  the  degree  specified. 


22  CONDENSATION    OF    VAPOR    AS    INDUCED    BY    NUCLEI    AND    IONS. 


In  table  9  I  have,  therefore,  arranged  the  data  for  n  with  reference  to 
the  corresponding  values  of  dp/p,  both  for  the  cases  of  I,  II,  III,  and  V, 
where  the  upper  pressure  limit  of  the  drop  dp  (curve  [dp]'),  and  cases 
F, .IF,  IV,  where  the  lower  pressure  limit  of  the  drop  dp  (curve  [dp]^, 
are  varied.  This  result  is  also  given  in  the  chart  (figs.  5  and  6)  and  the 
mean  results  of  the  latter  are  suggested  by  the  dotted  line  in  the  former. 

In  fig.  5  the  curious  result  is  obtained  that  the  data  for  [dp]'  are  now 
liable  to  lie  even  above  those  for  [dp^  which  is  the  inversion  of  the  former 
case.  As  a  whole,  however,  and  with  due  regard  to  the  subtleties  in- 
volved, the  two  sets  of  data  practically  belong  to  the  same  curve,  for 
the  departure  of  either  in  the  long  run  is  seen  to  be  positive  as  well  as 
negative.  The  results  of  fig.  5  (as  has  been  stated)  were  obtained  in  a 
single  series  of  observations,  all  at  the  same  temperature.  If  they  be 
compared  with  fig.  5  (dotted  line),  containing  observations  made  at 
other  times,  they  lie  distinctly  above  the  graph  of  the  figure,  no  matter 
whether  [8p/p]'  or  [dp/p^  is  in  question.  Hence  it  is  again  probable 
that  something  else  besides  mere  variation  of  the  barometer  is  in  question 
and  is  not  accounted  for  in  the  correction.  Thus  it  is  next  necessary  to 
inquire  into  the  effects  of  vapor  pressure,  which  in  series  I  and  II  would 
differ  from  series  I'  and  IF,  though  in  series  I,  II,  III,  IV,  and  V  the 
temperatures  are  so  nearly  alike  that  shifting  of  graphs  due  to  this 
disturbance  is  not  appreciable. 

TABUS  9. 


Summary  of  table  7.                Summary  of  table  8. 

. 

dp/p. 

nXio-3 
1'  and  II'. 

dp/p. 

nXio~3. 
I  and  II. 

dp/p. 

wXio-3. 
Ill  and  V. 

dp/p. 

wXio-3. 
IV. 

0.328 

2 

0.3II 

i 

0-333 

7 

0.329 

6 

•337 

15 

•313 

2 

•334 

24 

•339 

44 

•337 

15 

•331 

3 

•350 

H5 

•338 

10 

.... 

•353 

139 

•349 

93 

•348 

53 

•331 

4 

•358 

157 

.348 

53 

•332 

4 

•364 

179 

•364 

182 

•351 

76 

•339 

27 

•373 

242 

•373 

234 

•359 

120 

•340 

21 

•375 

244 

•375 

210 

•344 

39 

•383 

246 

^382 

327 

•384 

310 

•348 

72 

•394 

375 

•390 

372 

•399 

380 

•355 

104 

•395 

340 

•395 

340 

•437 

4IO 

•356 

116 

•356 

116 

•359 

105 

•  362 

106 

•364 

190 

14.  The  effect  of  vapor  pressure.—  The  second  extreme  limit, 


may  now  be  used  and  the  data  for  nucleation,  n,  expressed  in  terms  of 
dp~(n—nl)/(p—7r)    as   the   variable   for   comparison.      Remembering 


EFFECT  OF  VAPOR  PRESSURE.  23 

that  the  total  variation  of  pressure  to  bring  out  the  coronal  phenomenon 
does  not  much  exceed  3  cm.,  and  that  the  observations  below  will  be 
made  within  a  single  centimeter,  the  precipitation  of  moisture  may  be 
treated  as  depending  on  T/TJ,  the  ratio  of  the  initial  and  the  final  tem- 
perature of  adiabatic  cooling  if  the  former  is  nearly  constant  and  if  the 
same  medium  is  retained,  though  the  case  is  in  reality  more  complicated. 
These  data  are  also  given  in  table  9  and  have  been  inserted  in  fig.  7. 


FIG.  7. — Nucleation  found  at  different  drops  of  pressure.     Second  extreme  case. 

The  graphs  III,  IV,  and  V  are  now  even  more  coincident,  whereas  I 
and  II,  V  and  II'  differ  from  each  other  and  from  III  and  V  in  the  same 
sense  as  above.  Hence,  apart  from  barometric  pressure,  some  other 
cause  must  have  influenced  these  nucleations. 


CONDENSATION    OF   VAPOR   AS    INDUCED   BY    NUCLEI    AND    IONS. 


I  conclude,  therefore,  that  by  far  the  greater  part  of  the  dependence 
of  the  vapor  nucleation  upon  the  barometer  is  the  necessary  result  of 
the  thermodynamics  of  the  case,  but  that  conclusive  evidence  of  the 
absence  of  other  causes  either  within  or  without  the  fog  chamber  on  the 
time  variation  of  its  nucleation,  though  extremely  difficult  to  make  out, 
seems  as  yet  to  be  outstanding. 

15.  New  data  for  vapor  nucleation  in  the  lapse  of  time.  —  In  table  10 
results  of  the  same  character  as  the  preceding  have  been  collected. 
Moreover,  by  choosing  a  particular  dp  —  (TT  —  nJKp  —  7^=0.320  and 


reducing  all  data  for  n  to  this  value,  the  result  so  found  (w0-320X  io~3) 
should  be  independent  of  atmospheric  pressure,  etc.,  and  respond  to 
external  radiation  if  such  exists.  The  data  are  shown  in  fig.  8a.  They 
are  not  out  of  keeping  with  Wood  and  Campbell's  phenomena  as  a  whole, 
but  they  do  not  follow  the  barometer.  The  correction  of  n  is  about  i  .  7 
per  o.oo  i  of  the  pressure  ratio,  but  it  is  too  uncertain  in  this  region, 
since  the  graphs  are  of  pronounced  curvature. 

TABLE  10.  —  Time  variation  of  the  larger  colloidal  nucleation  of  wet  dust-free  air. 
Conical  filter.  Apparatus  II  with  2-inch  pipes,  cleaned  by  precipitation  before 
observation.  pm  =  o.i;  p  =  P—pm',  p  —  p2==I9-9- 


Date,  etc. 

dp. 

s. 

P. 

dp/p. 

nXio~3. 

dp-fr-Kj 

^O.KioXlO-3. 

p-n 

Aug.  6,   5hi6m 

25-7 

4.2 

76-7 

0-335 

21 

0.318 

24 

5  25 

25-7 

4.4 

76.7 

•336 

26 

•319 

28 

Aug.  7,  10  oo 

25-7 

4-3 

75-0 

•339 

24 

•323 

19 

10  10 

'25-7 

3-7 

75-9 

.338 

16 

•323 

II 

10  20 

25-7 

4.1 

75-9 

•339 

20 

•323 

15 

3  5 

25-7 

4-2 

75-7 

•340 

21 

.321 

19 

3  15 

25-7 

4-2 

75-7 

•340 

21 

•  321 

19 

Aug.  8,  10  40 

25.3 

3.6 

75-7 

•335 

H 

•317 

19 

10  50 

25-5 

4.0 

75-7 

•337 

18 

.320 

18 

II  OO 

26.0 

4-9 

75-7 

•344 

36 

•327 

24 

5  40 

25-9 

4-9 

75-7 

•342 

36 

•  325 

28 

25.6 

4-3 

75-7 

•339 

23 

.321 

21 

Aug-  9,   9  30 

25-6 

3-8 

75-8 

•338 

17 

.321 

15 

9  40 

25.8 

4.2 

75-8 

•341 

21 

•324 

14 

4  oo 

25-7 

4-5 

75-8 

•340 

27 

•319 

29 

4  i-o 

25-7 

23-9 

75-8 

•340 

2i8 

•319 

20 

4  20 

25-7 

5-i 

75-8 

•340 

40 

•319 

42 

1Not  cleaned  by  precipitation. 

Hence  in  table  1 1  a  larger  fiducial  value  (dp — [TT — 7rJ)/(/> — ?0  =0.335 
was  selected  in  turn,  as  the  graphs  in  this  part  of  the  field  (see  arrow  in 
fig.  7)  are  more  nearly  straight.  At  the  outset  complete  series  of  results 
(August  10,  n,  and  12)  were  investigated;  subsequently  but  three 
observations  in  the  neighborhood  of  the  abscissa  0.335  fullv  sufficed. 
The  completed  graphs  are  given  in  fig.  7  and  marked  VI  to  X.  Their 
position  is  throughout  low  as  compared  with  III  to  V,  for  which  there  is 


VAPOR    NUCLEATION    IN    LAPSE    OP    TIME. 
£ 

%  rf^N 


26 


CONDENSATION    OF   VAPOR   AS    INDUCED   BY   NUCLEI    AND   IONS. 


now  no  reason  referable  to  causes  within  the  fog  chamber,  unless  there 
exists  a  singularly  marked  temperature  effect,  presently  to  be  investi- 
gated. Series  VI  alone  is  peculiar,  showing  a  strong  initial  tendency  to 
return  to  the  earlier  set,  III  to  V.  Water  nuclei  were  precipitated 
before  each  observation.  The  data  for  w0-335  are  also  inscribed  in  fig.  8a 
and  fig.  86,  where  they  are  compared  with  the  barometer  and  the  tem- 
perature of  the  fog  chamber  in  a  general  way. 

Table  n  also  contains  the  corresponding  values  of  dp/p  and  the 
nucleations  n  derived  from  the  new  investigations  in  Chapter  IV.  From 
these  the  values  w0>340  for  £_/?/£  =  0.340  and  n0>345  for  dp/p  =  o.34$  are 
derived  to  be  used  in  the  correlative  summary  in  sec.  20.  The  nucleations, 
wo.345>  which  suffice  for  the  purpose,  are  given  with  the  others  in  figs.  8a 
and  86. 


isc/m. 


30° 


'  77 
',11. 


33 


27  Sift  29  1     Oct.    3  S  1  9  11  13  \5  11 

FIG.  86. — Changes  of  vapor  nucleation  of  dust-free    air,   barometric  pressure, 
temperature  of  the  fog  chamber  in  the  lapse  of  time. 


and 


The  data  for  n0  335  in  figs.  8a  and  86  sometimes  follow  the  barometer, 
sometimes  depart  widely  from  it;  but  coincidence  will  usually  occur  only 
when  both  accompany  the  same  temperature  effect.  As  a  rule  there  is  a 
rise  of  nucleation  from  morning  to  afternoon,  suggesting  the  phenome- 
non due  to  external  radiation  discovered  by  Wood  and  Campbell  (section 
i) ,  but  in  these  cases  temperature  is  also  apt  to  rise  coincidently.  The  rise 
in  question  fails  to  occur  but  4  times  out  of  the  13  observed  in  August, 
but  7  times  out  of  the  24  observed  in  September  (2  being  neutral),  and 
but  5  times  out  of  the  13  observed  in  October. 


VAPOR    NUCLEATION    IN    LAPSE    OF    TIME. 


ii. — Time  variation  of  the  larger  colloidal  nucleation  of  dust-free    wet    air.      Cor- 


responding  to  table  10,  with  allowance  for  temperature. 


=  p  —  p 


—  p2  = 


^>» 

A 

»/.-(*-*,) 

"033,X 

dp 

io-3 

Date,  etc. 

op. 

S. 

P- 

. 

P  . 

°io-3 

P 

W°io-3 

0 

Aug.  io,  9h3om 

25-7 

3-9 

75-8 

26.0 

0.323 

18 

1  (90)  r 

0-339 

13-3 

18.5 

4  40 

25-7 

3-9 

.... 

26.0 

•  323 

18 

( 

•339 

13-3 

35 

4  20 

25-7 

4-4 

75-6 

28.0 

.321 

25 

•340 

18.5 

4  30 

25-7 

4-4 

28.0 

.321 

25 

•340 

18.5 

.... 

4  40 

25-7 

4-4 

28.2 

.322 

25 

105 

•340 

18.5 

18.5 

25-3 

3-7 

75.6 

28.2 

.316 

16 

•335 

ii.  3 

35 

26.2 

5-7 

28.2 

.328 

55 

VT  < 

•347 

39-o 

27.6 

'9.6 

28.2 

•347 

190 

V  1.  ' 

•365 

185 

.... 

28.4 

2II.O 

28.2 

•359 

207 

•376 

280 

.... 

29.2 

•11.5 

.... 

28.2 

•370 

250 

.386 

320 

Aug.  ii,  8  50 

27-3 

75-5 

25.8 

•347 

130 

70 

•  362 

IOO 

15-2 

25-1 

2-3 

.... 

25.8 

•317 

3 

to 

•332 

2.6 

40 

25-7 

4.1 

25.8 

•325 

19 

65 

•340 

15-2 

27.0 

37-3 

.... 

26.0 

•343 

105 

VII. 

•  358 

83.5 

.... 

28.2 

4o.6 

.... 

26.0 

•359 

206 

•374 

253 

.... 

29-3 

2ii-5 

.... 

26.0 

•374 

250 

•388 

320 

.... 

30.2 

gyo 

26.0 

.386 

318 

.400 

5  0° 

25-3 

3-0 

75-4 

26.0 

.320 

7 

:  65  : 

•336 

5-5 

18.5 

2  c  7 

44, 

/y  f 

to 

•  ^4-0 

18.5 

38 

•O  •  / 

27  I 

•  *r 

*7  T. 

1,4.4. 

IOS 

1  80  ' 

OT" 

A  ^  •  O 

83.5 

o 

•*  /  •  •*• 
28.5 

I  •  o 
3II.O 

^6^ 

244. 

'378 

^O  O 

280 

29.2 

75-4 

•373 

T"T" 
248 

J 

*  O  / 

.387 

280 

.... 

or  y 

•386 

T.AT. 

AO2 

31.0 

6  J 

gy 

*  %3<->x-' 

•  398 

OT~O 
348 

.... 

.411 

.... 

.  . 

Aug.  12,  io  oo 

25-7 

3-1 

75*6 

26.0 

•  325 

8 

75 

•  340 

6.4 

6.4 

24  •  9 

2  .  I 

^14 

2.4 

-7  OQ 

1  .9 

33 

26.3 

26.i 

'^  ^ 

65 

.348 

49  .0 

28.4 

'10.5 



^362 

w  O 

195 

*  OT^ 

•  376 

245 

.... 

29-3 

3I2 

.... 

25.2 

•374 

248 

.... 

.388 

360 

3  30 

25-3 

2.6 

75-7 

25.8 

.320 

5 

80 

•334 

3-7 

30 

26.8 

47'4 

.... 

.  .  .  . 

•340 

105 

.... 

•354 

86.0 

50 

27-5 

.... 

.  .  .  . 

•  350 

142 

.... 

•363 

122 

28  4. 

2io.5 

.362 

207 

•375 

245 

.... 

*'*-'  .  <-| 

29-3 

3n-5 



.... 

*  O 

•374 

248 

.387 

320 

.... 

-JA    'I 

'  r  1 

44  •? 

4.1  c 

•453 

460 

OT-  '  <J 
42.8 

6IT, 

'  T-T-vJ 

T"   O 

4.  SO 

.565 

460 

4  30 

30.1 

'13 

76.2 

25-5 

'385 

*Td 

340 

.... 

•  398 

460 

Aug.  13,  io  oo 

25-9 

3-9 

24-3 

•326 

18 

56 

•  340 

13-3 

13-3 

26.6 

•335 

56 

•349 

39-o 

25 

27-3 

67.2 

.... 

•345 

104 

•358 

80.5 

.... 

3  30 

25-8 

3-7 

75-9 

24-3 

•  326 

16 

80 

•340 

"•3 

ii.  3 

26.3 

6-5 

•332 

78 

•347 

59-0 

45 

26.7 

7.0 

. 

•338 

96 

•  352 

74.0 

.... 

Aug.  14,  9  30 

25-5 
26.0 

3-5 

75-4 

23-9 

•324 
•331 

75 

J8o  j 

•338 
•345 

9-5 
56-5 

20 
56.5 

27.0 

87-5 

•344 

117 

/     1 

•358 

89.0 

3  15 

25-7 

4.0 

24.2 

•  329 

19 

60  r 

•341 

14.2 

IO 

26.2 

5-8 

75-2 

•334 

57 

•348 

41.0 

30 

26.7 

57-4 

. 

•341 

104 

J    I 

•355 

86.0 

.... 

Aug.  15,  9  40 

25-6 

75-4 

23-3 

•  326 

20 

1  65  I 

•339 

15-2 

18 

26.1 

5-3 

•333 

45 

.346 

31.0 

30 

26.9 

87  S 

•  344 

116 

J    [ 

•357 

89.0 

.... 

/  •  o 

O  T  T 

2wro. 


3  w'o. 


5gy'o.          flg. 


rgy- 


8gBP. 


28  CONDENSATION    OF   VAPOR   AS    INDUCED   BY    NUCLEI    AND   IONS. 

TABLE  n. — Time  variation  of  the  larger  colloidal  nucleation  of  dust-free  wet  air  —  Continued. 


dp-(ic-nj 

^o.335X 

dp 

W0.340X 

io-3 

Date,  etc. 

dp. 

s. 

P- 

t. 

P-K 

wXio  8. 

io-3 

P 

wXio  4. 

W0.348X 

io-8 

Aug.  15,  3hoora 
Aug.  1  6,  9  oo 

25-5 
26.0 
26.9 

25-7 
26.1 

27  I 

3-9 

s5'9 

87.i 

3-7 

4'o 

75-4 
76.0 

0 

23.8 
23.0 

0.324 
•331 

•343 
•325 
•330 
-244 

18 

45 
116 
16 
40 
117 

;( 
"( 

0.338 

•345 
•  357 
.338 
•343 

.  ^S7 

13-3 
43-0 

77-5 
"•3 
27-5 
74-.  O 

20 
43 

18 
33 

3  oo 

25.8 
26.2 

3-7 

C   -7 

75-8 

23.5 

•327 

•  ^32 

16 

4-S 

i"  \ 

•  340 

.  ^4S 

ii.  3 

31  .0 

"•3 

-21 

Aug.  17,  9  oo 

12  OO 

Aug.  23,  4  oo 

27.0 

25-7 
26.2 
26.8 

25-7 
25-9 
26.9 

25-7 
25  7 

87-3 
3-5 

84'9 

87.2 

3-0 

& 

4.8 

A.  8 

76^3 
76^2 
75-2 

23.2 

23^6 

25.0 

•343 
•323 
•330 
•338 
•323 
•  326 
•339 
•326 
326 

117 
12 

37 

100 

7-5 
34 
116 

34 

14 

n 

n 
i  " 

•356 
•337 
•343 
•351 
•337 
•340 
•353 
•342 
.  ^42 

83-5 
9-5 
24.6 
80.5 
5-5 
23-5 
80.5 
23-5 
23  .  s 

15 

38 

23-5 

45 

15 

^S 

Aug.  24,  9  30 

26.0 

27.0 

25-7 
26.2 

»i:I 

3-i 

C  A 

76'.i 

23.1 

•331 
•344 
•324 
•  33i 

56 
II7 

8.2 

48 

i  " 

•346 
•359 
•338 
•  344 

39-o 
66.5 
6.4 
32.7 

15 

3S 

3  oo 
Aug.  25,  9  oo 
3  oo 
Aug.  26,  9  oo 

27.0 

25-7 
26.2 
26.8 

25-7 
26.0 
26.9 
25-7 
26.0 
27.0 
25-7 

26  o 

'7.0 

4.0 

87-'4 
3-3 

4:1 

3-o 
4-7 
"6-7 
3-3 

A   -7 

76.2 
76.6 
76.4 

76  '.2 

24.0 
22.5 
23-5 
23-7 

•342 
•323 
•330 
•338 
•323 
•327 
•339 
•323 
•327 
•341 
•323 
^27 

117 

18 
46 
116 

10 

27 
88 
7-i 
32 
88 
10.5 
23 

n 

n 

n 
,«i 

•355 
•337 
•344 
•352 
•335 
•339 
•351 
.336 
•340 
•353 
•337 

.  ^41 

74.0 
14.2 
31.0 
86.0 
7-7 
19-5 
66.5 

5-5 

22.2 
64.0 

7-7 
17.5 

20 

40 

20 

40 

20 

38 

15 

33 

27  O 

»6  0 

T.AI 

105 

j    I 

•354 

69.5 

4  oo 
Aug.  27,  9  oo 

25-7 
26.1 
27.0 

25-9 
26.4 

4-o 
5-i 
106.7 
4.8 
96.8 

75-9 
75-3 

23.6 

23.7 

•324 
•330 
•342 
•330 
.336 

18 
40 
105 
34 
89 

n 
ri 

•338 
•344 
.356 
•344 
.350 

14.2 

27-5 
64.0 

23-5 
66.5 

78 
30 

18 
3° 

3  oo 

26.8 
25-9 

26  o 

•7.6 

"5-3 

96  2 

75-i 

23^8 

•342 
•331 

3^2 

116 

44 
67 

1  7°i 

•356 
•345 
.346 

94.0 
3i 

52 

20 

31 

27  O 

87  6 

.  ^46 

117 

j  i 

.360 

94 

Aug.  28,  9  oo 

25-9 
26  4 

*; 

75-6 

23.5 

•329 
.336 

21 

66 

J60J 

•342 
•349 

15-2 
49 

IO 

30 

3  oo 

27.0 

25-7 
26.3 

87-3 
4-5 
5.8 

75^6 

23.4 

•344 
•327 
•335 

117 

27 
58 

16,  r 

•357 
•340 
•348 

83-5 
19-5 
41.0 

19-5 
33 

Aug.  29,  9  30 
Sept.  7,  10  oo 

27.2 

25-9 
26.2 
26.8 
25-7 

26  o 

•4.6 

4-3 
5-4 

"7.2 

3-8 
c  a 

75-9 
75^6 

23-3 

22.0 

•347 
•328 
•332 
•340 
-328 
•332 

117 
24 
48 
104 
17 
44 

J     1 

"{ 

•  60  r 

.360 
•341 

•345 
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VAPOR    NUCLEATION    IN    LAPSE    OF    TIME.  29 

TABLE  n. — Time  variation  of  the  larger  colloidal  nucleation  of  dust-free  wet  air  —  Continued. 


Date,  etc. 

dp. 

s. 

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t. 

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13  WO. 


CONDENSATION    OF    VAPOR    AS    INDUCED    BY    NUCLEI    AND   IONS. 


TABLE  ii. — Time  variation  of  the  larger  colloidal  nucleation  of  dust-free  wet  air — Continued. 


ty-Or-TO 

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dp 

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wy. 


"wo. 


14wBrcor. 


VAPOR    NUCLEATION    IN    LAPSE    OF    TIME. 


31 


TABLE  n. — Time  variation  of  the  larger  colloidal  nucleation  of  dust-free  wet  air — Continued. 


Date,  etc. 

dp. 

s. 

/>• 

t. 

'/>  —  (TT  —  TTj) 
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11  wy. 


13W0. 


15  w  P  cor. 


*Room  heated  hereafter. 


32  CONDENSATION    OF    VAPOR   AS    INDUCED   BY    NUCLEI    AND   IONS. 

TABLE   ii. — Time  variation  of  the  larger  colloidal  nucleation  of  dust-free  wet  air — Continued. 


dp-  (---,) 

M0.335X 

dp 

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27.0 
26.O 
26.9 

27-4 
26.1 
26.6 

27.0 

"6.9 
3-6 

'1:1 

3-8 

5-i 
5.8 

76.6 
76^6 

19.0 

i'7'.6 

•348 
•331 
•343 
•349 
•334 
•34° 
•  346 

95 
15 
43 
118 

17 
40 
60 

1 
3° 

'"I 

•359 
•339 
•351 
•358 
•341 
•347 
•353 

69-5 
10.5 
29.0 

83-5 
12.3 

27-5 
41.0 

IO 

20 

8 

20 

Oct.  13,  9  oo 
6  30 
Oct.  14,  9  15 
Oct.  15,  9  oo 

26.0 
26.4 
27.0 
25.8 
26.6 
27.1 

25-7 
26.4 
27.2 
25-9 
26.5 
27  2 

2-3 
4.6 

5-3 

2.8 

4-5 
6-7 
3-0 

4-7 

6.2 

3-o 
5-0 
6  7 

77-4 

77-3 
77.1 

76  '-7 

18.0 

20.0 

20.  o 

20.4 

.328 
•333 
•341 
•324 
•335 
•341 
•324 
•333 
•344 
•327 
•335 
-14.5; 

3 
30 
46 
6 

28 
85 
7 
32 
69 
7 
38 
85 

, 

30 

.,, 

n 

•336 
•341 
•349 
•334 
•344 
•351 
•333 
•342 
•353 
•338 
•346 
•355 

2.6 

20.7 
31.0 
4-6 
19-5 
64.0 

5-5 

22.2 
52.0 

5-5 
26.0 
64.0 

15 

25 

13 

25 

15 

28 

IO 

23 

gy- 


?gBP. 


11  wy. 


13  wo. 


EFFECT    OF    BAROMETER,    TEMPERATURE,    AND    IONIZATION.  33 

16.  Effect   of   the    barometer. — If    we    look    more    specifically    at 
the  new  data  beginning  with  August  10,  coincidences  of  minima  and 
maxima  of  the  nucleation  with  maxima  and  minima  of  the  barometric 
pressure  occur  only  on  August  13,  25,  and  27,  and  these  are  not  pro- 
nounced.    In  September  there  is  no  detailed  similarity  until  September 
1 6,  but  both  curves  have  dropped  somewhat  toward  the  marked  mini- 
mum.   After  September  20,  however,  the  apparent  agreement  of  curves 
is  conspicuous  up  to  September  24  and  would  be  decisive  if  the  run  of 
temperature  were  not  similar.     During  the  remainder  of  the  month 
there  is  no  agreement — rather  an  opposition — and  the  two  curves  are 
remarkably  at  variance  during  the  unusually  low  barometer  in  the  early 
part  of  October.     The  peak  of  the  barometric  curves  from  October  4 
to  8  has  nothing  to  suggest  it  in  the  nucleation  curve.    We  may  conclude, 
therefore,  that  a  direct  barometric  effect  is  absent,  that  such  coincidences 
as  seem  to  occur  are  referable  to  other  causes,  and  that  the  method 
used  for  the  elimination  of  barometer  discrepancies  is  to  the  same  degree 
vouched  for. 

17.  Effect  of  temperature. — Throughout   all   of  the  observations  the 
tendency  of  temperature  of  the  fog  chamber  to  rise  from  morning  to 
afternoon  is  most  probably  to  be  regarded  as  the  cause  of  a  similar 
tendency  in  the  nucleation.    There  are  exceptions,  most  of  which,  how- 
ever, may  be  explained  away.    The  curves  show  a  similar  general  march 
from  August  10  to  23  and  from  here  to  August  29.     From  September 

7  to  1 8  there  is  much  detailed  agreement,  as,  for  instance,  on  September 

8  to  10  and  15  to  1 6.  The  same  is  true  after  September  20,  where  markedly 
coincident  variation  occurs. 

So  in  October  the  agreement  of  curves  is  apt  to  be  very  close,  as,  for 
instance,  the  effect  from  September  30  to  October  3,  the  general  fall 
thereafter,  and  the  effect  from  October  7  to  October  9.  All  of  this  will 
appear  more  strikingly  when  the  observations  are  averaged  for  several 
consecutive  days,  and  most  of  the  lack  of  synchronism  is  doubtless  due 
to  the  difficulty  of  finding  the  true  value  of  nucleation. 

18.  Effect   of   ionization. — To  find  whether  there  is  any  relation  of 
the  change  of  nucleation  in  the  fog  chamber  in  the  lapse  of  time  with  a 
state  of  ionization  of  the  atmosphere,  measurements  were  made  of  the 
latter  quantity  by  Miss  L.  B.  Joslin,  using  Ebert's  aspirator  apparatus. 
The  data  are  given  in  table  1 2 ,  where  V  denotes  the  fall  of  potential  during 
the  fiducial  time  of  aspiration  (about  10  minutes),  Q  the  charge  per  cubic 
centimeter,  and  n  the  corresponding  number  of  ions  per  cubic  centimeter. 
These  data  are  constructed  in  the  lower  curves  of  fig.  9,   together 
with  the  cotemporaneous  nucleations  and  temperatures  of  the  fog  cham- 
ber, on  a  somewhat  larger  scale  than  heretofore.    It  would  be  difficult  to 


34  CONDENSATION    OF   VAPOR   AS    INDUCED    BY    NUCLEI    AND   IONS. 

TABLE  12. — lonization  of  the  atmosphere  in  the  lapse  of  time — Ebert's  apparatus. 


Date. 

Time. 

V. 

Q. 

rcXio-3. 

Date. 

Time. 

V. 

Q. 

*Xio-3. 

Sept.  14 

ii  -3h 

9-3 

+0.53 

.56 

Sept.  29 

IO.Oh 

6-7 

+0.38 

I.  12 

8.2 

-  -47 

•38 

9.2 

-  .52 

i-53 

3-5 

10.8 

+  .61 

•76 

Oct.    i 

IO.O 

7-5 

+  .43 

.26 

12.6 

-  -7i 

.01 

8-9 

-  -51 

•50 

Sept.  15 

10.4 

8-3 

+  -47 

.40 

3-5 

6.2 

+  .35 

•05 

10.  I 

-  .58 

•  71 

4.8 

-  .27 

•79 

3-5 

9-9 

+  5-6 

.65 

Oct.   2 

IO.O 

6-5 

+  .37 

.09 

7-i 

-  .40 

.18 

9-6 

-  -55 

.62 

Sept.  17 

II  .0 

9.6 

+  .55 

.62 

3-5 

1.  1 

+  .06 

•19 

9.4 

-  -54 

•59 

7-2 

-  .41 

.20 

3-7 

6.8 

+  -39 

.14 

Oct.   3 

10.5 

8-3 

+  -47 

.40 

7-7 

-  .44 

.29 

2-3 

-  .13 

•38 

Sept.  1  8 

10.5 

3-6 

+  .20 

.60 

3-o 

7-7 

+  -44 

•29 

3-9 

—  .  22 

•65 

7-i 

-  .40 

.18 

3-5 

4-5 

+  -25 

.76 

Oct.   4 

3-5 

7-3 

+  .42 

.  21 

3-1 

-  .18 

•52 

2.8 

-  .16 

•47 

Sept.  19 

10.  0 

7-5 

+  -43 

1.26 

Oct.   5 

10.3 

6-7 

+  -38 

.  12 

7-7 

-  -44 

1.29 

7-8 

-  -45 

•32 

4.0 

7-3 

+  .42 

I  .  21 

Oct.   6 

10.5 

4-5 

+  .26 

.76 

2.4 

-  .14 

.41 

2.8 

-  .16 

•47 

Sept.  20 

10.3 

5-6 

+  .32 

•94 

Oct.   8 

IO.O 

14.0 

+  .80 

2-35 

3-7 

—   .  21 

•63 

10.6 

-  .60 

1.78 

3-5 

7-i 

+   .40 

1.18 

3-5 

7.6 

+  -43 

1.25 

5-i 

-   -29 

•85 

5-3 

-  -30 

.88 

Sept.  21 

IO.O 

6.0 

+  -34 

1.  00 

Oct.   9 

IO.O 

3-7 

+  .21 

•63 

6-9 

-  -39 

1.14 

4-2 

-  .24 

.70 

3-o 

5-6 

+  .32 

•94 

3-o 

4.0 

+  .22 

.66 

8.6 

-  .49 

i-44 

1.8 

—  .  10 

.31 

Sept.  22 

IO.O 

5-0 

+  .29 

•85 

Oct.   10 

IO.O 

7-8 

+  -44 

1.30 

14.9 

-  -85 

2.50 

3-3 

~  -19 

•56 

3-0 

6-5 

+  -37 

1.09 

3-5 

7-5 

+  -43 

1.26 

6-9 

-  -39 

1.14 

4.8 

-  -27 

•79 

Sept.  25 

12.5 

7.8 

+  -45 

1.32 

Oct.   ii 

10.3 

7-8 

+  -45 

1.32 

5-8 

-  -33 

•97 

4-7 

-  -27 

•79 

3-5 

3-9 

+   .22 

•65 

3-5 

7-i 

+  .40 

1.18 

1.8 

—  .10 

•3i 

2-5 

-  .14 

.41 

Sept.  26 

IO.O 

8-9 

+  .51 

1.50 

Oct.   12 

3-5 

5-9 

+  -34 

1.  00 

7-i 

-  .40 

1.18 

7.0 

-  .40 

1-17 

4.0 

3-6 

+   .20 

.60 

Oct.   13 

ii.  5 

6-7 

+  -38 

I.  12 

6.0 

-  -34 

i  .00 

ii.  3 

-  -65 

I.9I 

Sept.  27 

IO.O 

5-9 

+  -34 

i  .00 

3-5 

4.6 

+  .26 

.76 

3-6 

—  .  20 

.60 

3-5 

5-6 

+  .32 

•94 

Oct.   15 

10.2 

8-3 

+  -47 

I  .40 

2.8 

-  .16 

•47 

2-3 

-  -13 

•38 

Sept.  28 

3-5 

3-9 

+   .22 

•65 

3-5 

10.4 

+  -59 

i-74 

5-6 

-  -32 

•94 

2.4 

-  -14 

.41 

detect  any  detailed  similarity  in  the  two  sets  of  results.  Thus  the  maxi- 
mum of  nucleation  on  September  20  to  24  is  in  no  way  suggested  by  the 
ionization.  Both  curves  tend  to  descend  toward  the  end  of  the  month, 
but  this  may  be  due  to  causes  to  which  both  are  tributary.  As  such  an 
effect  will  appear  again  in  the  average  results,  it  may  be  dismissed  here. 
Fig.  9  also  contains  the  nucleations  nOS45  for  <^>/£  =  0.345  for  com- 
parison. Remarks  may  be  made  with  reference  to  them  similar  to  those 
just  stated.  The  enlarged  scale  admits  of  an  easier  comparison  of 
n0  335  and  n0  345,  which  hold  for  different  hypotheses. 


EFFECT    OF    IONIZATION. 


35 


CONDENSATION  OF  VAPOR  AS  INDUCED  BY  NUCLEI  AND  IONS. 


19.  Mean  results. — The  most  satisfactory  criterion  of  the  variation  of 
nucleation  in  the  lapse  of  time  would  perhaps  have  been  the  slope  of  the 
n  lines  as  given  by  the  three  observations  in  terms  of  the  abscissa, 
x=($p — [n — 7rJ)/(/> — ri)\  but  as  these  points  lie  on  a  graph  whose 
curvature  is  often  marked,  the  curvature  would  in  general  be  hard  to 
estimate  and  the  ordinate  w0335  for  #  =  0.335  nas  therefore  been  pre- 
ferred and  is  summarized  in  table  13. 

13. — Summary  of  table  9.     Observations  a.  m.  and  p.  m. 


Date. 

Tem- 
pera- 
ture. 

io-3. 

Date. 

Tem- 
pera- 
ture. 

"o.SSsX 

io-3. 

Date. 

Tem- 
pera- 
ture. 

"-0.335X 

io-3. 

o 

o 

o 

Aug.  io 

26 

90 

Aug.  25 

22 

70 

Sept.  12 

22 

50 

28 

105 

23 

60 

22 

65 

ii 

26 

70 

26 

24 

70 

13 

22 

55 

26 

70 

24 

70 

22 

50 

12 

26 

75 

27 

24 

75 

14 

22 

55 

26 

80 

24 

70 

22 

60 

13 

24 

56 

28 

24 

60 

15 

22 

55 

24 

80 

24 

65 

21 

40 

14 

24 

80 

29 

23 

70 

16 

20 

30 

24 

60 

Sept.   7 

22 

60 

20 

45 

15 

23 

65 

22 

70 

17 

21 

30 

24 

70 

8 

22 

55 

21 

37 

16 

23 

67 

22 

55 

18 

21 

40 

24 

65 

9 

21 

30 

20 

22 

50 

17 

23 

80 

23 

55 

23 

70 

24 

90 

IO 

23 

65 

21 

23 

85 

23 

25 

75 

23 

70 

23 

98 

24 

23 

75 

ii 

22 

55 

24 

95 

22 

55 

The  endeavor  may  be  made  to  test  the  value  of  n0  335  for  longer  inter- 
vals of  time.  As  the  series  is  often  interrupted,  2  -day  to  4-day  intervals 
for  the  present  suggest  themselves.  Consequently,  if  the  data  of  table 
13  (which  is  a  summary  of  table  ii)  be  so  compared,  the  values  given  in 
table  14  appear. 

If  the  results  of  table  13  be  further  corrected  for  dependence  of  the 
precipitation  on  the  changes  of  temperature  of  the  fog  chamber,  data 
given  in  an  earlier  report*  and  elsewhere  are  available. 

At  dp  =  22  cm.  the  amount  of  water  precipitated  per  cubic  centi- 
meter is  at 


4.2  5.5  6.7 

Hence  on  the  average  the  correction  may  be  taken  as  —  -  —  =  2.3  per 

5*5  X  20 

cent  of  the  values  of  m  at  20°  C. 


*Smithsonian  Contributions  No.  1651,  p.  135,  1905. 


MEAN    RESULTS. 


37 


Since  n  =  6ms3/xa?  approximately  (where  a  is  the  optical  constant 
of  coronas  and  5  their  angular  diameter  on  a  radius  of  30  cm.)  for  a 
given  s,  n  varies  as  m.  Therefore  n  must  be  increased  to  2  . 3  per  cent 
of  its  value  per  degree  of  temperature  of  the  fog  chamber  above  20° 
C.  In  this  way  the  corrected  data  of  table  14  were  found. 

TABLE  14. — Nucleations  (averaged  in  groups  of  2  to  4  days)  in  the  lapse  of  time. 
wXio~3  at  <W£  =  o.345/  and  at  dp—(K  —  Tt^)/(p  —  ^=0.335. 


Date. 

Tem- 
pera- 
ture. 

Barom- 
eter. 

W0.335. 

Cor- 
rected 

W0.335. 

^0.345. 

Cor- 
rected 

W0.345. 

lonization. 

+  n. 

—  n. 

°C. 

cm. 

Aug.  10-13 

25-8 

75-71 

77,000 

87,000 

37,600 

43,ooo 

14-17 

23-8 

75-71 

72,000 

78,000 

38,000 

41,900 

23-26 

23-6 

76.07 

73,000 

79,000 

35,900 

39,100 

27-29 

23-8 

75-50 

68,000 

74,000 

31,400 

34,400 

Sept.    7-10 

22.3 

75-44 

57,000 

60,000 

31,600 

33,4oo 

11-13 

22.  O 

75-98 

56,000 

59,000 

30,500 

32,000 

14-16 

21  .  2 

76.47 

47,000 

49,000 

32,200 

33,200 

1600 

1570 

17-20 

21.6 

76.08 

45,000 

47,000 

3O,OOO 

31,200 

1090 

900 

21-23 

22.5 

75-72 

75,000 

79,000 

4O,OOO 

42,500 

970 

1550 

24-27 

19.6 

76.63 

37,000 

37,000 

28,500 

28,200 

IOOO 

790 

28-30 

I9.O 

76.37 

37,000 

37,000 

29,200 

28,500 

885 

1230 

Oct.     i-  3 

18.0 

76.  10 

32,000 

30,000 

25,400 

24,100 

1040 

I  IIO 

4~  5 

20.8 

75-75 

44,000 

45,000 

28,300 

28,900 

1167 

395 

6-  7 

20.  6 

74-85 

40,000 

41,000 

27,500 

27,900 

760 

470 

8-  9 

20.3 

76.08 

36,000 

36,000 

26,300 

26,500 

1220 

920 

IO-II 

19.7 

75-17 

35,ooo 

35,ooo 

26,300 

25,100 

I26O 

640 

12-13 

18.7 

76.97 

27,000 

27,000 

22,500 

21,800 

960 

I22O 

H-I5 

20  .  2  !  76  .  90 

40,000 

40,000 

25,500 

25,600 

1570 

4OO 

1 

1  These  will  be  considered  in  section  20. 

Table  14  also  contains  the  data  for  the  corresponding  averages  of 
temperature,  barometric  pressure,  and  ionization,  and  all  data  have 
been  further  given  in  the  graphs  fig.  10,  with  the  times  (abscissas)  laid 
off  on  a  smaller  scale  to  bring  out  the  relative  variations.  It  is  again 
apparent  that  no  relation  of  the  nucleation  curve  to  the  barometer 
curve  or  to  the  ionization  curve  can  be  made  out.  On  the  other  hand, 
the  vapor  nucleations  of  the  dust-free  wet  air  in  the  fog  chamber  agree 
very  fully  with  the  cotemporaneous  variations  of  the  temperature  of 
the  fog  chamber  (not  of  the  temperature  of  the  atmospheric  air  without, 
of  which  they  are  also  independent).  It  is  even  possible  to  make  out 
the  rate  at  which  nuclei  are  produced  when  the  temperature  of  the  fog 
chamber  increases.  Taking  the  mean  trend  of  both  curves  (nuclei  and 
temperature),  it  appears  that  nearly  8000  colloidal  nuclei  are  generated 
(apparently)  in  dust-free  wet  air,  by  a  rise  of  temperature  of  i°  C. 


20.   Nucleations  depending  upon    dp/p. — In    the    above    experiments 
the  nucleations  were  compared  at  a  fixed  value,  0.335,  of  tne  variable 
n)'      If.   however,   the   corresponding  value   of   the 


38          CONDENSATION    OF   VAPOR   AS    INDUCED   BY    NUCLEI    AND   IONS. 

relative  drop  dp/p  (which  assumes  that  all  the  water  vapor  is  expanded 
adiabatically  without  condensation)  be  computed,  the  latter  will  vary 
with  temperature  in  a  way  correlative  with  the  vapor  pressures  con- 
tained in  the  former.  The  nucleations  computed  for  this  particular 
series  of  values  of  dp/p  will  also  vary,  and  the  rate  was  found  to  be  about 
6000  nuclei  per  degree.  This  is  so  near  the  temperature  effect  given 
in  section  19  that  there  must  be  a  common  cause  underlying  both. 


FIG.  10. — Vapor  nucleation  of  dust-free  air,  temperature  of  fog  chamber,  barometric 
pressure,  and  positive  and  negative  ionization  (the  former  with  small  circles)  in 
lapse  of  time,  averaged  for  period  two  to  four  days. 

Hence  in  table  n,  n  was  also  computed  in  its  dependence  on  dp/p, 
and  advantage  was  additionally  taken  of  the  new  values  of  n  given  in 
Chapter  III  for  the  higher  coronas.  Two  fiducial  values  of  the  variable 
dp Ip  were  tested;  the  former,  dp/p  =  o.$4o,  being,  as  a  rule,  too  small, 
the  latter,  dp/p  =  0.345,  was  selected.  The  tables  contain  both  of  the 
corresponding  values  of  nucleation,  n0  340  and  n0  345;  but  the  last  only 
has  been  given  on  the  charts  (figs.  8,  9,  and  10).  The  other  does  not 
differ  essentially  from  it.  All  values  are  summarized  in  succession  in 
table  15. 


NUCLEATIONS    DEPENDING    ON    RELATIVE     DROP    IN    PRESSURE.        39 

Fig.  8  contains  an  extended  comparison  of  the  old  curve  for  n0  336  and 
the  new  curve  for  w0-345,  under  the  conditions  which  are  given.  In  their 
narrower  variations  the  two  curves  are  similar  and  the  details  already 
specified  for  n0  335  need  not  therefore  be  repeated  for  nQ  345.  Pronounced 
maxima  and  minima  will  in  particular  be  found  coincident. 

The  same  will  be  observed  in  the  case  of  fig.  9,  where  a  larger  scale  is 
introduced  for  n0  335.  The  question  of  greatest  interest  is  now  the  com- 
parison of  mean  data  such  as  are  given  in  table  14  in  the  lapse  of  time. 

The  data  for  w0  345  have  been  corrected  for  the  effect  of  temperature 
/,  on  the  amount  of  water  precipitated,  by  taking  from  the  recent  results 
referred  to  the  temperature  coefficients  dn/ndt,  example  of  the  values 
for  different  relative  drops  being 

dp/p=  o.i  0.2  0.3  0.4  0.5 

io3dn/ndt=  14  18  23  27  30 

These  data  would  not,  however,  seriously  modify  the  trend  of  the 
curves. 

The  graph  (fig.  10),  which  also  contains  these  nucleations,  shows  that 
the  effect  of  temperature  in  the  lapse  of  time  has  not  been  eliminated 
by  replacing  the  extreme  variable  (dp  —  [TT  —  Kj)/(p  —  TT)  by  the  other 
extreme  variable  dp  /p.  In  other  words,  if  the  nucleation  corresponding 
to  a  fixed  exhaustion  dp/p  =  o.34$  is  studied  in  the  lapse  of  time,  the 
successive  nucleations*  show  a  dependence  on  the  temperature  of  the 
fog  chamber  which  can  no  longer  be  explained  away.  Both  the  details 
and  the  general  character  of  the  graphs  for  n0  345  follow  the  fluctuations 
of  temperature  to  an  extent  which  may  be  estimated  from  the  figure  as 
an  increment  of  about  2000  nuclei  per  rise  of  temperature  of  i°  C.  at 
about  20°  C.  and  for  dp/p  =  0.345.  Finally,  there  is  no  adequate  reason 
why  the  effect  of  cooling  below  a  higher  surrounding  temperature  should 
be  more  efficient  than  the  corresponding  effect  below  a  slightly  lower 
temperature;  for  the  rate  of  reheating  would  depend  on  the  difference 
of  temperatures. 

21.  Possible  suggestions  as  to  the  temperature  effect.  —  To  obtain  a 
suggestion  as  to  the  reason  of  the  apparent  increase  of  the  size  of  col- 
loidal nuclei  with  rise  of  temperature  (c&t.  par.)  effectively,  therefore, 
of  their  apparent  increase  in  number  at  a  given  supersaturation,  it 
is  expedient  to  recall  the  form  of  Helmholtz's  modification  of  Kelvin's 
vapor-pressure  equation.  If  the  ratio  r  of  pressures  at  a  convex  surface 
r  and  at  a  plane  surface  be  pr/P^,  R  the  gas  constant  of  water  vapor, 
#  its  absolute  temperature,  s  the  density,  and  T  the  surface  tension  of 
the  liquid, 


*  American  Journal,  xxm,  1907,  10,  p.  209. 


CONDENSATION    OP    VAPOR   AS    INDUCED    BY    NUCLEI    AND    IONS. 


TABLE  15. — Corresponding  to  table  n,  but  containing  nucleations  for  dp/p  =  0.340 

and  dp/p  =  0.345. 


Date. 

Tem- 
perature. 

W0.34<)X 

io-3. 

W0.34oX 

io-3. 

Date. 

Tem- 
perature 

W0.34()X 

io-3. 

W0-34sX 

io-3. 

Aug.   10 

26 

18.5 

35 

Sept.   20 

22.  2 

15 

25 

28 

18.5 

35 

23.0 

15 

45 

ii 

25-8 

15.2 

40 

21 

23-5 

3(?) 

40 

26 

18.5 

38 

23.0 

IO 

38 

12 

26 

6.4 

33 

22 

22.  O 

9-5 

25-8 

30 

50 

22.  2 

IO 

40 

13 

24-3 

13-3 

25 

23 

22.3 

10? 

40 

24-3 

ii.  3 

45 

23.0 

25 

40 

14 

23-9 

20 

56 

24 

21 

10 

25 

24.2 

10 

30 

20.8 

13 

25 

15 

23-3 

18 

30 

25 

19.6 

15 

40 

23-8 

20 

43 

19.0 

15 

30 

16 

23.0 

18 

33 

26 

18.2 

10 

30 

23-5 

n-3 

3i 

20.0 

12 

23 

17 

23.2 

15 

38 

27 

I9.O 

IO 

30 

23-6 

23-5 

45 

19-5 

15 

25 

23 

25.0 

15 

35 

28 

19.0 

IO 

20 

24 

23.1 

15 

35 

19-5 

15 

25 

24.0 

20 

40 

29 

19.  2 

15 

35 

25 

22.5 

20 

40 

18.8 

15 

25 

23-5 

20 

38 

30 

19.0 

IO 

30 

26 

23-7 

15 

33 

19.2 

15 

40 

23-6 

18 

30 

Oct.    i 

16.8 

10 

20 

27 

23-7 

18 

30 

17.2 

IO 

26 

23-8 

20 

3i 

2 

17.0 

6.4 

28 

28 

23-5 

10? 

30 

18.0 

10 

25 

23-4 

19-5 

33 

3 

18.5 

13 

28 

29 

23-3 

13 

33 

20.5 

20 

53 

Sept.    7 

22.  O 

12.3 

35 

4 

20.5 

15 

28 

22.  O 

15-2 

40 

21.0 

10 

25 

8 

22.  O 

15-2 

30 

5 

20.8 

9-5 

30 

22.0 

15-2 

28 

21.0 

10 

30 

9 

21.0 

8 

20 

6 

20.5 

10 

35 

22.6 

13 

30 

21.0 

20 

10 

22.8 

10 

35 

7 

21.0 

30 

23.2 

IO 

35 

2O.  O 

25 

ii 

22.  O 

15 

30 

8 

18.8 

8 

20 

22.  2 

13 

30 

21.5 

9-5 

30 

12 

22.  0 

15 

25 

9 

20.  o 

13 

25 

22.  2 

18 

40 

21.0 

10 

30 

13 

22.2 

10.5 

33 

22.0 

ii.  3 

25 

IO 

I9.8 

.... 

30 

20.0 

.... 

25 

H 

22.2 

17 

33 

ii 

18.0 

7 

20 

22.2 

18 

35 

21.0 

30 

15 

22.0 

13 

30 

21.0 

13 

30 

12 

19.0 

IO 

20 

16 

I9.8 

13 

30 

17.6 

8 

20 

2O.  O 

12 

35 

13 

18.0 

15 

25 

20.0 

13 

25 

17 

20.5 

8 

20 

21.0 

3 

30 

14 

20.0 

15 

28 

18 

21  .O 

18 

30 

15 

20.4 

10 

23 

TEMPERATURE  EFFECT — CONCLUSION.  41 

whence  it  appears  that  the  increment  of  &  and  R  may  replace  each 
other. 

A  small  radius  at  a  high  temperature  is  as  effective  as  a  larger  radius 
at  a  low  temperature  $,  and  that  is  substantially  what  the  above  data 
have  brought  out.  Naturally  the  equation  has  been  pushed  beyond  its 
limits,  for  the  meaning  of  T  for  particles  not  large  as  compared  with 
molecular  dimensions  is  obscure;  but  it  appears  in  other  cases  and  is 
probably  true  here  that  the  suggestions  of  the  equation  are  trustworthy 
in  a  general  way.  Computing 


by  the  aid  of  the  adiabatic  equation  we  may  write  ioV  =  i 
(PrlPj  where  Iog10  pr/P00  =  o.8,  and  $1r  =  2/io5,  nearly.  But  ^  =  262° 
if  the  gas  is  originally  at  temperature  /  =  2o°,  whence  r  =  75/io9.  Since 
dr/r= — dtfj/i?!,  an  increment  of  the  radius  of  but  0.038  under  the 
given  conditions  is  equivalent  to  a  rise  of  temperature  of  i°  C.  of  the  air 
within  the  fog  chamber  or  to  2000  more  available  nuclei,  according  to 
the  above  figure. 

22.  Another  suggestion. — The   increment    of  about   2000  nuclei  per 
degree  of  temperature  under  the  conditions  given  may  also  be  looked 
on  as  a  parallel  to  what  occurs  in  case  of  a  radiant  field  like  that  pro- 
duced by  the  X-rays.    One  may  regard  ionization  as  a  state  of  dissocia- 
tion sufficiently  advanced  to  set  free  electrons  and  from  this  point  of 
view  equivalent  to  a  very  high  degree  of  temperature.     One  may  thus 
expect  a  passage  of  the  vapor  nuclei  of  wet  dust-free  air  into  the  ions 
through  a  continuous  gradation  of  nuclei,  and  may  note  that  vapor 
nuclei  and  ions  always  occur  together.     True,  the  latter  have  been 
associated  with  the  radiation  penetrating  the  atmosphere,  with  good 
reason,  but  the  possibility  of  a  collateral  cause  of  the  ionization  within 
the  fog  chamber  may  nevertheless  be  entertained. 

23.  Conclusion. — It  is  shown  by  direct  observation  that  the  number  of 
nuclei  caught  in  dust-free  wet  air  at  low  barometer  pressure  is  greatly  in 
excess  of  the  number  caught  (cat.  par. )  at  high  barometer.  This  result  may 
be  accounted  for  as  a  necessary  consequence  of  the  thermo-dynamics  of 
the  experiment,  however  large  and  unexpected  the  variations  appear. 

The  comparison  of  the  nucleation  of  dust-free  air  with  the  cotempo- 
raneous  changes  of  atmospheric  ionization  shows  no  correspondence 
whatever.  This  is  curious,  because  the  ions,  though  much  fewer  in 
number,  are  larger  in  size  than  even  the  larger  colloidal  nuclei,  and 
therefore  capture  much  of  the  moisture  at  low  exhaustion.  One  must 
conclude  that  the  variations  of  the  ionization  are  not  sufficient  to  be 
detected  in  the  presence  of  the  other  nucleation. 


42  CONDENSATION    OF   VAPOR   AS    INDUCED    BY    NUCLEI    AND    IONS. 

For  the  same  reason  would  it  be  unwarrantable  to  look  for  effects 
due  to  variations  of  any  external  radiations.  In  other  words,  it  is 
improbable  that  Wood  and  Campbell's  phenomena  can  be  detected  by  the 
fog  chamber,  and  the  results  which  seemed  at  first  in  accord  with  it 
are  due  to  a  rise  of  temperature.  The  results  show  that  dp/p  is  a  suitable 
variable  for  the  comparisons  of  nucleations  in  a  plug-cock  fog  chamber 
like  the  above. 

Finally  the  temperature  conditions  within  the  fog  chamber  produce 
a  very  definite  effect,  amounting  to  an  increase  (cceteris  paribus*)  of 
about  2000  available  vapor  nuclei  per  degree  centigrade  near  20°  and 
the  given  exhaustion^  7^  =  0.345  orvi/v  =  i  .35.  Estimating  the  average 
number  of  efficient  nuclei  present  at  25,000,  this  amounts  to  an  incre- 
ment of  about  8  per  cent  per  degree.  Anomalous  as  it  may  seem  that 
rise  of  temperature  should  increase  the  number  of  efficient  nuclei  (cat. 
par.},  probably  by  increasing  their  size  throughout,  nothing  has  been 
suggested  to  explain  this  result  away.  Virtually  the  same  thing  is  done 
by  radiation,  though  in  much  more  marked  degree  than  by  temperature, 
so  that  one  might  regard  ionization  as  a  state  of  dissociation  sufficiently 
advanced  to  set  free  corpuscles,  or  equivalent  to  a  high  degree  of 
temperature.  One  might  therefore  expect  a  passage  of  the  vapor  nuclei 
of  wet  dust-free  air  into  the  ions,  through  a  continuous  gradation  of 
nuclei;  and  in  fact  (granting  that  other  valid  explanations  for  the 
occurrence  of  ions  have  been  given) ,  they  always  occur  together. 

The  present  and  a  variety  of  other  results  made  it  necessary  to  re- 
standardize  the  coronas  in  terms  of  the  number  of  nuclei  represented, 
and  the  work  will  be  given  in  the  next  chapter.  Some  of  these  data 
have  already  been  utilized  in  the  above. 


CHAPTER  III. 

THE  NUCLEATION  CONSTANTS  OF  CORONAS. 
RESULTS  WITH  A  SINGLE  SOURCE  OF  LIGHT. 

24.  Introduction. — At  this  point  it  seemed  essential  to  restandardize 
the  coronas  in  terms  of  the  numbers  of  nuclei  represented  by  a  given 
angular  aperture  and  type  of  corona  at  a  given  exhaustion  and  tem- 
perature.     The   measurements*   carried   out   for   this   purpose   in   my 
earlier  memoirs  were  made  under  very  different  conditions ;   and  though 
reductions  to  the  present  results  are  feasible  in  a  measure,  it  will  ob- 
viously be  preferable  to  repeat  the  work  anew.     This  is  particularly 
the  case  because  the  corrections  referred  to  are  liable  to  be  large  and 
because  the  results  in  the  following  chapters  will  essentially  depend 
on  the  number  of  fog  particles  per  cubic  centimeter.     This  datum  will 
here  as  elsewhere  be  called  the  nucleation,  and  in  dust-free  wet  air  the 
types  of  nuclei  present  will  be  the  ions  and  the  vapor  nuclei  only.    These 
will,  as  a  rule,  be  inefficient  in  the  presence  of  phosphorus  nuclei. 

25.  Apparatus  and   methods. — The  apparatus  used   is   the   same   as 
heretofore  described  in  the  Carnegie  Institution  of  Washington  Publica- 
tion No.  62,  p.  74,  and  is  shown  in  fig.  n.    It  consists  of  a  large  vacuum 
chamber    V  connected  with  the   relatively  small  fog  chamber  F,  the 
volume  ratio  being  about  v/V  =  o.o6.     The  latter  was  cylindrical  in 
form,  with  its  long  axis  horizontal,  so  as  to  admit  of  the  measurement  of 
coronas  of  large  aperture.     This  angle  may  exceed  60°  in  the  extreme 
cases  and  there  must  be  some  depth  (exceeding  5  inches)  if  the  coronas 
are  to  be  sufficiently  intense.    The  need  of  large  fog  chambers  is  there- 
fore apparent  and  the  plug-cock  fog  chamber  seems  to  be  the  only 
apparatus  adapted  to  the  present  purposes. 

The  connecting  pipe  was  about  18  inches  long,  2  inches  in  diameter, 
and  the  stopcock  2  inches  in  bore.  Phosphorus  nuclei  were  used.  To 
guard  against  subsidence  and  undersaturation,  the  cloth  lining  of  the 
fog  chamber  was  fitted  close  to  the  walls  and  but  two  opposite  narrow 
horizontal  strips  were  left  open  for  the  observation  of  coronas. 

The  method  used  was  the  one  previously  employed.  The  highly 
nucleated  medium  (5X10°  phosphorus  nuclei  per  cubic  centimeter)  was 
successively  expanded  by  a  fixed  amount,  and  the  nucleated  air  removed 
from  the  fog  chamber  was  replaced  by  filtered  air.  The  residual  nuclea- 

*Smithsonian  Contributions,  No.  1373,  vol.  29,  pp.  i  to  173,  1903;  ibid.,  No.  1651, 
vol.  34,  pp.  i  to  226,  1905. 

43 


44 


CONDENSATION    OF   VAPOR    AS    INDUCED    BY   NUCLEI    AND    IONS. 


tion  therefore  varies  in  geometric  progression  with  the  number  of  ex- 
haustions, apart  from  necessary  corrections.  The  observations  were 
made  in  time  series  by  two  observers,  Mise  L.  B.  Joslin  assisting  me  with 


FIG.   ii. — Fog  chamber  F,  and  vacuum  chamber  V. 

the  work.  Details  will  be  given  in  connection  with  the  data.  The 
initial  isothermal  (r)  pressures  p  and  pf  of  the  fog  and  vacuum  chambers 
and  the  final  isothermal  (r)  pressure  p3,  when  in  communication  after 
exhaustion,  were  carefully  determined  previous  to  the  experiment  with 
coronas.  These  were  needed  for  the  computation  of  the  amount  of 
water  precipitated  per  cubic  centimeter  in  each  of  the  series  of  exhaus- 
tions. In  addition  to  this  the  pressure  [/>J  for  finding  the  ratio  of  the 
geometric  sequence  was  necessary  and  found  as  follows:  In  each 
exhaustion  the  stopcock  was  opened  suddenly  at  the  beginning  of  each 


NUCLEATION    CONSTANTS    OF    CORONAS.  45 

minute  and  kept  open  for  5  seconds;  it  was  then  closed  until  the  end 
of  the  minute.  Hence  [p2]  is  the  isothermal  pressure  observed  in  the 
fog  chamber  under  the  given  conditions,  determining  the  density  of  air 
and  the  nucleation  left  after  each  exhaustion.  The  ratio  is  therefore 

(i) 


where  TT  is  the  vapor  pressure  at  the  given  isothermal  temperature  r  of 
observation. 

As  soon  as  the  exhaust  cock  was  closed  the  filter  cock  of  the  fog 
chamber  was  opened,  in  order  to  evaporate  the  fog  particles  with  the 
least  amount  of  subsidence  or  other  loss.  Observation  of  aperture  was 
made  during  the  5  seconds  in  question. 

The  relative  number  of  nuclei  for  a  series  of  coronas  of  decreasing 
aperture  is  obtained  in  this  way.  It  is  furthermore  necessary  to  stand- 
ardize one  of  the  coronas  absolutely.  This  was  done  as  described  in  the 
earlier  work  (Smithsonian  Contributions,  No.  1651),  and,  if  d  denotes 
the  diameter  of  the  fog  particles  and  s  the  chord  of  the  angular  diameters 
(j)  of  the  corona  observed  with  a  goniometer  with  a  radius  of  30  cm., 

2  sin  0/2=5/30  (2) 

^5  =  0.0032  (3) 

was  accepted  when  the  eye  and  the  source  of  light  were  at  distances 
D  =  3o  and  250  cm.,  respectively,  on  opposite  sides  of  the  fog  chamber. 
With  a  constant  a  selected  we  may  then  compute  the  nucleation  nf 
for  the  smaller  white-centered  or  normal  coronas  as 

,     6m  3  (4) 

Vl/ x  o 

xa 

where  m  is  the  amount  of  water  precipitated  per  cubic  centimeter  in  the 
exhausted  vessel  and  nf  the  number  of  nuclei  per  cubic  centimeter  so 
computed.  The  theory  of  diffraction  would  give  a  collateral  approxi- 
mation 

6m  m 

=  71(73.2  v03==  0.205(10*!? 

26.  Equations  and  corrections. — In  the  present  experiment  no  cor- 
rection was  made  for  the  time  loss  of  nuclei,  for  convection  losses 
during  influx  and  efflux  (vortices  washing  against  the  walls  of  the 
vessel) ,  nor  for  evaporation  loss  (loss  of  water  nuclei  on  evaporation  such 
as  occurs  with  ions  but  not  with  solutional  nuclei  like  those  here  pro- 
duced by  phosphorus,  etc.).  The  justification  of  this  was  tested  by 
making  series  of  measurements  with  widely  different  exhaustions, 
[dp2],  both  as  to  the  amount  of  the  latter  and  number  of  exhaustions  in 
the  series,  as  will  be  shown. 


46 


CONDENSATION    OF    VAPOR   AS    INDUCED    BY    NUCLEI    AND    IONS. 


TABLE  16. — Coronas  standardized.  Phosphorus  nuclei.  Bar.  77.7  cm.;  temp.  20°. 
Cock  open  5  seconds ;  time  between  observations  60  seconds ;  dp'  =18.2;  dps=  17.0; 
[d/>J=i6.2  at  5  seconds,  16.8  at  60  seconds;  ^=0.779;  S=j.2;  0  =  0.0032; 
D  =  30  cm.  and  250  cm. 


No. 

Corona. 

s. 

I0-3n'  = 
o.  igos3. 

w0Xio-3 
ratio. 

wXio-3. 

^=0.0183 

Xw~1/3. 

s'  =  a/d. 

i 

Fog 

4010 

4010 

0.000115 

27.8 

2 

r'fog 

30 

3230 

124 

25-8 

3 

r'  fog 

2420 

135 

23-7 

4 

r'  fog 

.... 

1840 

149 

21.5 

5 

we 

.... 

1390 

164 

19-5 

6 

W  V 

.... 

.... 

1050 

1  80 

17.8 

7 

dkb 

.... 

.... 

791 

196 

16.3 

8 

Gbp 

H 

.... 

.... 

594 

220 

H-5 

9 

g'bp 

13 

.... 

.... 

446 

241 

13-3 

10 

gyo 

13 

.... 

333 

264 

12.  I 

ii 

yo 

ii 

.... 

248 

291 

II.  0 

12 

we 

10 

.... 

183 

321 

10.  0 

13 

w  p 

8.1 

.... 

132 

359 

8.9 

H 

gbp 

7-5 

.... 

91.8 

406 

7-9 

15 

w  o 

7.0 

65" 

4090 

62.2 

462 

6.9 

16 

cor 

6.1 

43 

4170 

4i-3 

529 

6.0 

17 

5-4 

30 

4630 

25-9 

618 

5-2 

18 

4-3 

15 

3960 

15-2 

738 

4-3 

19 

3-2 

6.2 

3440 

7-2 

948 

3-4 

20 

2.O 

i-5 

3680 

1.6 

.001564 

2.O 

21 

I  .O 

.  2 

2170 

•4 

2473 

1-3 

17.  —  Coronas  standardized.  Phosphorus  nuclei.  Barometer  77.7  cm.;  tem- 
perature 20°.  Cock  open  5  seconds;  60  seconds  between  observations;  dp'  =18.2; 
dp3=ij.o;  [dp^\=i6.2  after  5  seconds;  16.8  after  60  seconds.  Distance  30  cm. 


and  250  cm.;  goniometer  radius  30  cm.;  ^=0.779;  S=6.8;1 


0.0032. 


No. 

Corona. 

s. 

io3nf  = 
0.  igos3. 

w0Xio~3 
ratio. 

wXio-3. 

^  =  0.0183 
Xw~1/3. 

sf  =  a/d. 

i 

R'fog 

5100 

5100 

0.000106 

30.0 

2 

R'fog 

30 

3950 

116 

27.6 

3 

R'fog 

3050 

126 

25-4 

4 

wR' 

.... 

.... 

2350 

138 

23.2 

5 

wr 

.... 

.... 

.... 

1790 

151 

21.2 

6 

w  v 

.... 

.... 

.... 

1360 

165 

19.4 

7 

St.  b 

.... 

.... 

.... 

IO2O 

181 

17.7 

8 

B.  P. 

.... 

.... 

769 

202 

15-8 

9 

gbp 

.... 

579 

220 

14-5 

10 

gyo 

13 

.... 

435 

241 

13-3 

ii 

w  o 

11.7 

.... 

32.7 

265 

12.  I 

12 

w  r  o 

10.5 

.... 

241 

295 

IO-9 

13 

wP 

9.0 

.... 

176 

327 

9.8 

T4 

g'BP 

7.8 

.... 

.... 

125 

366 

8.8 

15 

w  o 

7-5 

80 

4710 

87 

4l6 

7-7 

16 

wb  r 

6.8 

60 

5160 

59 

470 

6.8 

17 

.... 

5-9 

39 

5060 

39 

540 

5-9 

18 

(late) 

4-9 

22 

4660 

24-7 

630 

5-i 

19 

(early) 

4-2 

14 

5200 

13-7 

766 

4.1 

20 

3-4 

7-4 

5760 

6-5 

980 

3-2 

21 

.... 

2.4 

2.7 

6530 

2.  I 

.001430 

2.  2 

22 

.... 

1.8 

I.I 

8260 

•  7 

.  002030 

1.6 

xUse  mean  5=  7.2  as  in  table  16. 


NUCLEATION     CONSTANTS    OF    CORONAS. 


47 


zzo 


£00 


»  o 


10 


FIG.  12. — Nucleation  n,  in  terms  of  the   apertures   of  coronas. 
Small  nucleation,  moderate  exhaustion. 


10         ft         44-        16         IB 


200 


1000 


10  1Z  14  16  18  20          22  24          26  2Q  30 

FIG.   13. — Nucleation  n,  in  terms  of  the  apertures  of  coronas.     Large 

nucleations,  moderate  exhaustions. 


48  CONDENSATION    OF    VAPOR    AS    INDUCED    BY    NUCLEI    AND    IONS. 

The  chief  corrections  are  for  subsidence  of  fog  particles  and  for  the 
change  of  m  with  a  drop  of  pressure  and  temperature.  For  a  rectangular 
vessel  of  height  h,  subsidence  loss  during  a  time  t  may  be  written  vt/h, 
where  v  is  the  rate  of  subsidence  in  centimeters  per  second.  Since 
io~8v  and  ds  =  a,  it  may  also  be  written  for  the  fixed  time  t 


h       a2  ~52 

where  5  is  the  subsidence  constant  for  the  loss  during  the  fixed  time  t. 
Hence  for  a  rectangular  vessel 

1 


and  for  a  cylindrical  vessel  of  radius  r  and  horizontal  axis 


equations  which  will  be  useful  below. 

In  the  present  case  we  may  therefore  write  the  nucleation  obtained 
in  successive  identical  exhaustions  beginning  with  n0 


(8) 


as  further  explained  in  the  earlier  volume.  Again,  since  for  normal 
coronas  nz  is  supposed  to  be  given  by  n  =  6ms3/xa3,  S  may  be  computed 
by  two  successive  exhaustions  as 


Hence  the  terms  of  the  series 


6m 

may  also  be  computed,  and  since  nz= — -3  s3z,  the  equation 

nd 

6ms  z  i 

W"=  (10) 


NUCLEATION    CONSTANTS    OF    CORONAS.  49 

is  available  for  computing  the  initial  nucleation  «0,  and  hence  all  sub- 
sequent nucleations,  absolutely.  Naturally  a  number  of  observations 
nz  and  sz  will  be  used  for  computing  nQ  and  5.  The  equation  shows  very 
well  how  the  constants  n0,  S,  a,  m,  are  involved. 

From  nz  the  diameter  dz  of  the  2th  fog  particle  may  then  be  computed 

dz=n~I/li/6m/7:  (n) 

and  similarly  the  2th  aperture  se  will  be,  since  ds  =  a 


to  be  compared  with  the  observed  value  of  sz.  It  is  clear  that  d  and  5 
will  be  independent  of  m,  while  n  varies  directly  with  it.  Examples  of 
all  these  relations  will  be  found  in  the  following  section. 

27.  Data  for  moderate  exhaustions. — These  data  are  given  in  tables 
1 6  and  17.    The  drop  of  pressure  is  17  cm.  and  the  barometer  unusually 
high  at  77.7    cm.      Consequently   the  relative   drop  is   dp3/p  =  o.2ig 
an.dv1/v  =  i.ig,  temperature  20°  C.     The  symbols  denote  dp'=p — //, 
dp3  =  P — Pai  [$p2\  =P —  [Pz]>  as  explained  in  sections  25  and  26,  where  the 
meaning  of  y,  a,  5,  D,  etc.,  will  also  be  found. 

The  first  column  shows  the  number  z  of  the  exhaustion,  the  second 
and  third  the  selected  annuli  of  the  coronas  and  their  apertures  s,  meas- 
ured to  the  outer  edge  of  red  or  the  first  annuli.  In  the  fourth  column 
n'  =  6ms*/na3,  while  the  fifth  shows  successive  values  of  nQ  and  their 
mean.  The  sixth  column  gives  the  computed  absolute  nucleation,  the 
seventh  the  corresponding  diameter  of  the  fog  particle,  and  the  eighth 
the  computed  aperture  s.  The  data  have  been  left  as  originally  com- 
puted, for  their  relations  are  chiefly  of  interest;  but  the  value  of 
m  =  3 .  2  X  io~8  here  used  is  too  small  and  will  be  corrected  in  section  34. 

These  data  are  shown  graphically  in  figs.  12  and  13,  the  computed 
values  of  5  being  taken  as  abscissas,  the  computed  n  as  ordinates.  To 
admit  the  enormous  range  of  the  nucleation  n  the  ordinates  are  appro- 
priately changed  in  the  scale  of  10.  The  observed  data  are  given  in 
the  same  diagram,  but  with  a  different  designation  for  the  points. 

28.  Remarks  on  the  tables  and  charts.— One    may  observe  at  the 
outset  that  the  initial  nucleation  n  is  about  the  same  in  both  cases, 
being  n  =  5, 100,000  and  4,010,000  smaller  in  the  second.     The  same 
order  of  values  will  be  found  for  the  nucleations  n  in  very  different  orders 
of  exhaustions  in  the  succeeding  tables. 

The  following  values  of  S  were  computed  as  shown  in  equation  9 
from  the  data  of  tables  1 6  and  1 7 : 


50  CONDENSATION    OF    VAPOR    AS    INDUCED    BY    NUCLEI    AND    IONS. 

5  =  7.0          6.1  5.4          4.3          3.2          2.0          i.o 

5=  7-4          3-9        10.4          8.7          6.9          3.3 

*=7-5          6.8          5.9         4.9          4.2          3.4          2.4          1.8 
S=          2.0         7.6         9.1         4.8         5.8         5.8         2.9 

Leaving  out  the  smallest  coronas  and  those  which  are  no  longer  normal, 
the  data  5  =  y.2  and  5  =  6.8  were  taken  as  fair  averages  in  the  two 
cases.  The  data  for  n0  show  that  the  first  table  (16)  is  somewhat  over- 
compensated,  while  the  second  (17)  is  undercompensated  by  the  values 
of  5  entered.  The  high  value  of  [dp2]  =  i6.8  was  accepted  with  mis- 
givings, but  there  is  no  evidence  against  it.  It  is  interesting  to  com- 
pare with  the  above  values  of  5  those  which  may  be  computed  from  sub- 
sidence data  in  the  way  given  in  equation  7.  From  this  it  appears  that 
5  =  1.7  for  £  =  5  seconds  of  subsidence  of  fog.  Now,  the  time  needed  for 
complete  evaporation  was  about  15  or  20  seconds,  whence  it  follows  that 
5  must  be  of  the  order  of  5  to  7  ,  agreeing  therefore  very  well  with  the 
datum  computed  from  coronas.  For  the  very  small  coronas  subsidence 
is  too  rapid  to  enter  into  any  correction  of  this  kind. 

The  selection  of  a  constant  a  =  cfc  =  o.oo32  is  the  weakest  part  of  the 
above  deduction.  It  is  based  on  the  earlier  memoir  and  obtained  from 
the  subsidence  of  observed  coronas.  Since  the  theory  of  diffraction 
for  an  angular  radius  <j>  of  the  coronas  gives 

sin  ^>  =5/60  =  1.22  X/d  (13) 

for  the  first  minimum  annulus  of  wave-length  X,  and  ds  =  a, 

a  =  73.2^  (14) 

whence  a  =  o  .  0032  would  correspond  to  blue  violet.  With  an  eye  at  but 
30  cm.  from  the  fog  chamber,  the  equation  for  sin  <j>  is  certainly  not  quite 
true  and  a  must  be  variable  with  X,  except  perhaps  for  the  smaller  normal 
coronas,  which  are  so  closely  packed  that  a  mean  value  of  X  is  suggested. 
If  m  be  taken  as  3.2Xio~~6,  equation  4  shows  ^'  =  190  s3.  Equation 
1  4  incorporated  in  equation  4  would  imply  for  i  o6  m  =  3  .  2 


_ 
= 


6ms3 

7r(73.2  /I) 


n'  =  0*036  s  w1  = 

according  as  the  first  red,  orange,  or  violet  minimum  were  used,  data  which 
merely  imply  an  order  of  values,  as  equation  13  is  not  fully  applicable. 
Tables  16  and  17  and  figs.  12  and  13  show  a  satisfactory  order  of 
agreement  between  the  observed  and  computed  values  of  5  and  the 
corresponding  data  computed  for  n  as  far  as  5  =  7  to  10  cm.,  where  the 
middle  green  coronas  enter.  The  agreement  thereafter  improves  again 
until  the  higher  green  coronas  are  passed,  when  further  divergence  is 
marked.  I  will  not  enter  into  this  here,  as  the  subject  has  been  discussed 


NUCLEATION    CONSTANTS     OF    CORONAS.  51 

in  the  earlier  memoir.  It  is  necessary,  moreover,  to  investigate  some 
other  method  of  obtaining  5  for  the  very  large  coronas,  such  as  is  given 
in  Chapter  IV.  In  the  present  memoir  the  discrepancy  is  accentuated 
by  the  short  periods  of  i  minute  between  the  observations.  This  is  not 
sufficient  for  the  complete  mixture  of  the  inflowing  air  and  the  nucleated 
air  within  the  fog  chamber.  As  a  result  there  are  apt  to  be  color  dis- 
tortions and  bands  of  color  before  the  real  corona  appears,  while  the 
latter  is  not  quite  sharp.  It  was  thought  that  longer  intervals  of  waiting 
between  the  exhaustions  would  have  introduced  other  discrepancies 
or  losses  of  nuclei.  Experiments  made  under  these  conditions  did  not, 
however,  much  improve  the  irregularities,  as  may  be  seen  in  section  36. 
Furthermore,  in  the  larger  coronas  it  is  difficult  to  determine  the  actual 
limits  of  the  diffused  annuli  by  the  present  single-source  method.  The 
same  difficulty  will  appear  in  the  next  section.  Finally  the  d  and  s 
values  computed  from  equations  n  and  12  show 

^  =  0.0183  n~1/3  s  =  o. 175  ni/3 

For  the  lower  coronas  these  s  values  agree  with  the  observed  data 
quite  within  the  errors  of  observation,  remembering  that  the  coronas 
were  not  perfectly  sharp.  For  the  higher  coronas  they  are  probably 
close  to  the  truth,  provided  the  green  and  blue  coronas  be  measured 
to  the  purple  rings.  Both  d  and  s  will  be  discussed  below  and  another 
reduction  will  be  attempted. 

29.  Data  for  low  exhaustions. — Inasmuch  as  the  only  correction 
added  was  for  subsidence,  it  is  necessary  to  test  in  how  far  convection 
losses  of  nuclei  upon  evacuation,  losses  on  evaporation,  and  losses  in 
the  lapse  of  time  (decay)  are  relatively  small.  This  may  be  done  by 
comparing  the  data  for  very  low  exhaustions  with  the  data  for  relatively 
high  exhaustions.  In  the  former  case  many  exhaustions  must  be  made 
and  a  longer  time  will  elapse  between  the  first  and  last  of  the  equal 
intervals  than  in  the  second  case,  where  there  will  be  relatively  few 
exhaustions  and  a  relatively  small  lapse  of  time.  If  the  errors  in  question 
are  negligible,  the  same  initial  nucleation  and  the  same  diameter  of  fog 
particles  for  the  same  coronas  will  be  obtained.  The  subsidence  constant 
5  appears  as  follows: 

*  =  6.  5.8         5-4         4-8      -4-i         3-3         2.7         2.0         i.o 

15.4         2.6         5.5         6.7         6.8         3-9         3-9 

6.2         6.0         5.3         4-5         4-o         3-3         2.5         1.7 
5=         4.1  —         7-6         8.4         3-8         5-8         5-5         4-i 

The  mean  values  are  ^  =  6-8,  52  =  4-9-  Hence  5  =  5-9  was  taken. 
Experiments  showed  [dp2]  for  5  seconds  of  opening  of  the  exhaust  cock 
to  be  equivalent  to  ?  =  0.873.  The  computed  diameter 


52  CONDENSATION    OF    VAPOR   AS    INDUCED   BY   NUCLEI    AND    IONS. 

iO 


1ZOO 


3000 


ZOOO 


1000 


8  9  10          11 


FIG.  14.  —  Nucleation  n,  in  terms  of  the  apertures  of  coronas.    Low  nucleations; 
low  exhaustions. 

FIG.  15.  —  Nucleation  n,  in  terms  of  the  apertures  of  coronas.    High  nucleation; 
low  exhaustion. 


NUCLEATION    CONSTANTS    OF    CORONAS. 


S3 


18. — Coronas  standardized.     Phosphorus  nuclei.     Bar.  75.1  cm.;    temp.  26°; 
60  seconds  between  observations;    cock  open  5  seconds.     dp'=io.']\    dp3=io.o; 
9-2;   ^=0.873;   5  =  6.8;   a  = 


No. 

Corona. 

s. 

I03W'  = 
O.I28.J3. 

w0Xio~3 
(ratio)  . 

wXio-3. 

Xw11/3. 

s'=a/d. 

i 

Rfog 

30 

2540 

2540 

0.000118 

27 

2 

Rfog 

26 

.... 

2  2OO 

124 

25-9 

3 

Rfog 

25 

.... 

.... 

1880 

131 

24.4 

4 

Rfog 

22 

.... 

1630 

137 

23-3 

5 

Rfog 

22 

I4OO 

144 

22.2 

6 

wR' 

19 

1210 

150 

21.3 

7 

!  wR 

17 

1030 

159 

2O.  I 

8 

!  we 

16.5 

.... 

163 

19.6 

9 

*w  c 

15-5 

'748 

177 

18.1 

10 

1v 

.... 

.... 

635 

186 

17.2 

ii 

Blue 

14-5 

.... 

.... 

537 

199 

16.1 

12 

gBP 

H 

.... 

.... 

454 

209 

15-3 

13 

gBP 

13-8 

.... 

.... 

383 

222 

14.4 

14 

gBP 

13-8 

.... 

.... 

322 

233 

13-7 

15 

gyo 

13-5 

.... 

271 

247 

12.9 

16 

'gyo 

13-5 

228 

264 

12.  I 

17 

yo 

12-5 

191 

278 

n-5 

18 

yr 

ii.  5 

.... 

.... 

1  60 

298 

10.8 

19 

we 

10.5 

.... 

.... 

132 

316 

IO.  2 

20 

wP  cor 

9-7 

.... 

.... 

108 

335 

9.6 

21 

gBP 

8.1 

.... 

.... 

88 

362 

8.8 

22 

gBP 

7-6 

.... 

68.7 

393 

8.1 

23 

7-3 

53-0 

428 

7-5 

24 

.... 

6.9 

42.0 

2650 

40.3 

470 

6.8 

25 

5-8 

25-0 

2100 

30.2 

6.2 

26 

5-4 

20.  I 

2430 

21  .  I 

584 

5-5 

27 

4.8 

14.2 

2560 

I4.I 

665 

4-8 

28 

8.8 

2590 

8.6 

785 

29 

.... 

3-3 

4.6 

2580 

4-5 

976 

3-3 

30 

.... 

2-7 

2.6 

2880 

2-3 

.001220 

2.6 

31 

.... 

2.O 

1  .0 

1810 

1.4 

H38 

2.2 

32 

.... 

I  .O 

.  I 

2970 

•9 

1660 

i  -9 

33 

.... 

.0 

.0 

4850 

•  5 

2038 

1.6 

II.    Same.    Bar.  75.  4  cm.;  temp.  24°  C.;  5  =  4.9. 

i 

Fog 

2120 

O.OOOI25 

25-6 

2 

Fog 

30 

.... 

1850 

131 

24-3 

3 

Fog 

24 

.... 

.... 

1610 

138 

23-2 

4 

Rfog 

23 

.... 

.... 

1390 

144 

22.2 

5 

Rfog 

21 

.... 

I2IO 

150 

21-3 

6 

Rfog 

18 

1040 

1  60 

20.0 

8 

Rfog 
Cfog 

17 
16 

.... 

.... 

893 
767 

168 
176 

19.0 

18.2 

9 

Cfog 

15 

.... 

658 

185 

17-3 

10 

v-c 

14 

.... 

561 

195 

I6.4 

ii 

Violet 

.... 

.... 

477 

207 

15.5 

12 

B 

14 

.... 

406 

218 

14.7 

13 

g-b 

.... 

346 

230 

13.9 

H 

gbp 

14 

.... 

294 

241 

13.3 

15 

g'bp 

14 

.... 

.... 

251 

256 

12-5 

16 

gyo 

13 

.... 

213 

268 

II.  9 

17 

gyo 

13 

.... 

181 

288 

ii.  I 

1  Mixed  colors. 


54          CONDENSATION    OF    VAPOR   AS    INDUCED   BY    NUCLEI    AND    IONS. 

TABLE  18 — Continued. 


No. 

Corona. 

s. 

io3w'  = 

0  128S3. 

w0Xio-3 
(ratio)  . 

wXio-3. 

d=o.oi6i 

XM-l/3 

s'=a/d. 

18 

wo 

12.0 

.... 

153 

O.OOO3OI 

10.6 

19 

wo 

ii.  3 

129? 

322 

9.9? 

20 

we 

10.7 

109 

335 

9.6 

21 

w  c 

IO.O 

9i 

358 

8-9 

22 

wP 

9.0 

75 

382 

8.4 

23 

g'bp 

8.0 

62 

407 

7-9 

24 

g'bp 

7-5 

50 

438 

7-3 

25 

w  r 

6-7 

38^5 

2060 

40 

47i 

6.8 

26 

we 

6.2 

30.5 

2090 

30-9 

513 

6.2 

27 

cor 

6.0 

27.6 

2490 

23-5 

563 

5-7 

28 

cor 

5-3 

19.1 

2290 

17.7 

617 

5-2 

29 

cor 

4-5 

ii.  6 

1930 

12.8 

688 

4-6 

30 

cor 

4.0 

8.2 

2070 

8.4 

793 

4.0 

31 

cor 

3-3 

4-6 

1910 

5-i 

936 

3-4 

32 

cor 

2-5 

2.0 

1720 

2-5 

.001180 

2.7 

33 

cor 

i-7 

.6 

2690 

•5 

2040 

1.6 

34 

cor 

.0 

.0 

.  i 

3500 

•9 

The  data  of  table  18  are  arranged  as  above  for  table  16.  The  adiabatic 
drop  of  pressure  is  10  cm.  from  75.1  cm.  and  the  relative  drop  therefore 
dp3/p  =  o.  133  and  the  volume  expansion  about  v1/v  =  i .  107.  The  water 
precipitated  per  cubic  centimeter  is  about  m  —  2 . 2  grams  per  cubic 
centimeter,  in  both  series  at  26°  and  24°.  Hence  w  =  0.12  8s8.  A  more 
recent  value  of  m  will  be  inserted  for  definite  purposes  in  section  34. 

These  data  are  given  in  the  charts  (figs.  14  and  15)  with  a  usual 
distinction  between  observed  and  computed  values  of  the  coronal 
apertures  5.  The  divergence  again  begins  in  the  region  of  green  coronas, 
but  is  here  on  opposed  sides  of  the  line  computed  for  the  two  series.  The 
reason  of  this  is  the  lack  of  homogeneity  of  the  wet  nucleated  air,  when 
the  interval  between  observations  is  but  i  minute.  The  colors  of  coro- 
nas are  mixed  and  the  individual  observations  to  this  extent  uncertain. 
With  these  differences  the  periods  occur  in  the  usual  way. 

An  interesting  result  of  this  series  is  the  occurrence  of  crimson  and  red 
coronas  of  the  first  order,  above  the  violet.  In  other  words  the  initial  fogs 
soon  dissolve  into  true  coronas.  But  their  size  is  difficult  to  estimate 
in  case  of  the  single-source  method,  because  of  their  filmy  character. 

One  may  note  that  the  initial  nucleations  ^0  =  2,320,000  and  2,470,000 
correspond  to  the  values  of  the  table  19. 

30.  Data  for  high  exhaustions. — The  corresponding  results  for  an 
adiabatic  drop  of  pressure  of  27 .  i  cm.  from  75  cm.  are  found  in  table  19. 
There  are  three  series.  The  relative  drop  of  pressure  is  ^3/^  =  0.273, 
the  volume  expansion  v1/v  — 1.2^4.  Hence,  in  the  absence  of  phos- 
phorus nuclei,  precipitation  will  take  place,  in  the  given  apparatus,  on 


NUCLEATION     CONSTANTS     OF    CORONAS. 


55 


the  nuclei  of  dust-free  air,  which  are  within  reach  of  the  exhaustion  to 
the  extent  of  about  n  =  57,000.  Coronas  can  not  be  brought  to  vanish, 
but  up  to  the  final  limit  the  water  nuclei  are  alone  active.  The  amount 
of  water  precipitated  per  cubic  centimeter  at  25°  was  taken  as  w  = 
4.iXio~6.  Hence  n'  =  0.242  sa.  The  subsidence  constants  appear  as 


^=7.4    5.8        4.9 
S=     14.6     2.7 


7-2     6.3         5.3 
—  i.i       3.6 


4.6 


7-3         5-6         5-0 
16.4       —2.0 


an  irregular  series  of  values,  due  to  the  increasing  efficiency  of  the  vapor 
nuclei  of  dust-free  air.  The  values  of  5  found  in  tables  16  and  17  are 
therefore  taken  in  preference.  The  observed  drop  [3p2]  corresponds  to 
y  =  0.656.  The  diameter  of  particles  is  d  =  o.oi^gn~l/3.  The  value  of 
m  taken  will  be  replaced  by  a  more  recent  value  in  section  34. 

TABLE  19. — Coronas  standardized.    Phosphorus   nuclei.     Bar.  75.0  cm.;    temp.  25°; 
60  seconds  between  observations;    cock  open  5  seconds,     dp'  =  27.1;    dp  3=20.5; 
25.0;   ^  =  0.656;   8  =  6.5  assumed;   0  =  0.0032. 


No. 

Corona. 

w'io~3  = 

O.  24.2S3. 

w0Xio-3. 

wXio~3. 

rf  =  W-l/3X 
0.0199. 

s'  =  a/d. 

I. 

i 

Rfog 

20 

2320 

2320 

0.000150 

21.3 

2 

we 

15 

1500 

173 

18.5 

3 

violet 

15-5 

955 

202 

15-8 

4 

Gbp 

15 

.... 

608 

235 

13-6 

5 

gy° 

H 

.... 

387 

273 

11.7 

6 

w  r 

10.5 

.... 

.... 

246 

317 

IO.  I 

7 

Pcor 

8.6 

.... 

.... 

152 

373 

8.6 

8 

w  o 

7-4 

98 

2510 

90.8 

442 

7-2 

9 

cor 

5-8 

42.2 

2080 

1     52-5 

532 

6.0 

10 

*cor 

4-9 

28.5 

2370 

/     27.9 

657 

4-9 

ii 

cor 

4.8 

26.6 

(4610) 

13-4 

840 

3-8 

II. 

i 

Fog 

2470 

2470 

0.000148 

21.6 

2 

R'fog 

23 

.... 

1610 

170 

18.8 

3 

Fog 

1040 

197 

16.3 

4 

gbp 

16 

673 

227 

14.1 

5 

g'o 

430 

264 

12.  I 

6 

yo 

ii.  8 

272 

307 

10.4 

7 

w  P  cor 

9-3 

170 

359 

8.9 

8 

w  y 

7.2 

90-3 

2160 

103 

424 

7-5 

9 

cor 

6-3 

60.5 

2520 

593 

5io 

6-3 

10 

cor 

5-3 

36.1 

2730 

32.6 

624 

5-i 

ii 

xcor 

4.6 

23-5 

(3530) 

16.4 

783 

4.1 

12 

D.  F.  air 

6.1 

54-9 

.... 

.... 

III. 

I 

Fog 

23 

2270 

2270 

0.000152 

21.0 

2 

Rfog 

1470 

175 

18.3 

3 

violet 

J7 

.... 

95i 

202 

15-8 

4 

gbP 

15 

.... 

610 

235 

13-6 

5 

gy  o 

13.6 

.... 

.... 

388 

273 

ii.  8 

6 

w  r 

10.6 

246 

317 

10.  1 

7 

w  P  cor  ? 

8.0 

.... 

.... 

152 

373 

8.6 

8 

w  o 

7-3 

94.1 

2390 

89.5 

445 

7-2 

9 

cor 

5-6 

42.6 

1880 

5i-4 

535 

6.0 

10 

cor 

25-0 

29.7 

2530 

26.7 

666 

4.8 

1  Nuclei  of  dust-free  air  and  water  nuclei  remain  constant. 

2  Nuclei  of  dust- free  air  in  presence  of  water  nuclei. 


CONDENSATION    OF   VAPOR   AS    INDUCED   BY    NUCLEI    AND    IONS. 


The  preceding  data  are  shown  in  fig.  16,  with  a  distinction  between 
the  observed  and  computed  values  of  s.  The  usual  difficulties  due  to 
impure  colors  are  apparent.  In  view  of  the  high  exhaustions  many 
typical  coronas  do  not  appear  and  the  small  coronas  are  lost  by  the 
efficiency  of  vapor  nuclei  as  stated. 

4        6         8        10 


600 


soo 


4  6  6  10  ft  14-          16  18  20          22          £4 

FIG.  16. — Nucleation  n,  in  terms  of  the  apertures  of  coronas.    High  exhaustion. 

31.  Standardization   with   ions. — The    endeavor    to    standardize    the 
coronas  by  precipitating  the  fog  particles  upon  ions  lead  to  peculiar 
results,  which  makes  it  necessary  to  discuss  the  subject  independently  in 
Chapter  V.     In  fact,  about  one-half  of  the  water  nuclei  which  should  be 
present  after  the  first  evaporation  of  fog  particles  vanishes  independently. 
Half  the  ions  are  thus  not  represented  by  fog  particles,  except  in  the 
first  precipitation.    The  remainder  in  the  subsequent  exhaustions  behave 
more  normally. 

32.  Further  data. — Results  obtained    in    case    of    the   intermediate 
exhaustions  dpz  =  ~Lhj  cm.  are  liable  to  be  most  serviceable  for  the  con- 
struction of  a  practical  table,  and  two  further  series  were  therefore 
investigated  under  atmospheric  conditions  different  from  the  above. 
These  results  are  given  in  table  20  and  in  figs.  17  and  18.    In  both  series 
the  agreement  between  the  observed  and  computed  values  of  5  within 
5  =  10  is  surprisingly  close.     The  attempt  was,  moreover,  to  compute 
tables  1 6  and  17  under  modified  suppositions,  putting  [§p2]  =  I^-3  as 
in  table  20  and  then  reducing  all  data  to  24°.     The  results  are  of  no 
marked  advantage  over  the  earlier  data  and  are  therefore  omitted. 


NUCLEATION     CONSTANTS     OF    CORONAS. 


57 


FIG.  1 7. — Nucleation  n,  in  terms  of  the  apertures  of  coronas.    Low  nucleation, 
moderate  exhaustion. 


15  17  13  Z1  Z3  If 


31 


FIG.  1 8. — Nucleation  n,  in  terms  of  the  apertures  of  coronas.  High  nucleation, 
moderate  exhaustion. 


CONDENSATION    OF   VAPOR    AS    INDUCED   BY    NUCLEI    AND    IONS. 


TABLE  20. — Coronas  standardized  with  phosphorus  nuclei.  Bar.  76.2  cm.;  temp. 
24°  C.;  cock  open  5  seconds;  60  seconds  between  observations.  <^>'=i8.i  cm.; 
dpa=  ll  • l  >  [$p2\=  J6  •  3  after  60  seconds;  distances  40  cm.  and  250  cm. ;  goniometer 
arms  30  cm.;  y  =  o.j8;  5  =  6.5;  ds=^2. 


No. 

Corona. 

ioV  = 

1  0.2I0^3. 

w0Xio~3 
(ratio). 

wXio~3. 

d  =  n~Vs 
Xo.019. 

s'  =  a/d. 

I. 

i 

Fog 

(30) 

5302 

5302 

0.000108 

30.0 

2 

Fog 

25 

4110 

119 

27.2 

3 

w  o 

17 

3180 

129 

25.0 

4 

w  o 

17 

2470 

141 

23.0 

5 

W  0 

17 

1900 

153 

21.  I 

6 

wr  o 

16 

1470 

167 

19.4 

7 

v 

895 

198 

I6.3 

8 

b 

16 

686 

216 

15.0 

9 

bg 

16 

524 

235 

13-8 

10 

wy  o 

15 

397 

258 

12-5 

ii 

wr  o 

13 

301 

284 

xi.  4 

12 

we 

u-5 

226 

312 

10.4 

13 

wP 

10 

167 

345 

9-4 

H 

cor 

8 

122 

383 

8-3 

15 

.... 

7 

72.0 

4470 

85-5 

43i 

7-5 

16 

.... 

6-5 

57-7 

5300 

57-8 

491 

6-5 

17 

.... 

5-7 

38.8 

54io 

38.1 

564 

5-7 

18 

4-9 

24.8 

5530 

23-8 

660 

4-9 

19 

4.0 

13-4 

5260 

13-5 

800 

4.0 

20 

3-2 

6-9 

5840 

6-3 

0.001027 

3-2 

21 

2.6 

3-7 

11070 

1.8 

1560 

2.  I 

22 

i-5 

•7 

5970 

.6 

3170 

i-5 

No. 

Corona. 

s. 

I03W'  = 

o.2io-y3. 

n0=io~3. 

wXio-3. 

d  =  n~V3 
Xo.oi9. 

s'  =  a/d. 

II. 

j 

Fog 

4040 

4040 

O.OOOI2O 

27.0 

2 

wr' 

(is)  ' 

3130 

130 

24.8 

3 

we 

.... 

.... 

2410 

138 

22.8 

4 

!  w  r 

17.0 

.... 

1860 

154 

20.9 

5 

w  c 

16.5 

.... 

1430 

168 

19.2 

6 

V 

.... 

.... 

1090 

184 

17-5 

7 

bg 

16.5 

.... 

.... 

836 

202 

16.1 

8 

g 

16.0 

.... 

.... 

635 

221 

14.6 

9 

gy 

481 

242 

13.0 

10 

w  o 

14.0 

361 

267 

12.  2 

ii 

w  r 

ii  .0 

268 

295 

IO.9 

12 

w  c 

IO.O 

198 

326 

IO.O 

13 

cor 

9.0 

144 

363 

9-0 

H 

7-9 

.... 

.... 

104 

404 

8.0 

15 

.... 

7-i 

75-2 

4200 

72.4 

456 

7.0 

16 

.... 

5-8 

41  .0 

3370 

49.1 

520 

6.1 

17 

.... 

5-3 

31-3 

4090 

30.9 

605 

5-4 

18 

.... 

4-5 

19.1 

4160 

18.5 

717 

4-5 

19 

3-5 

9.0 

3710 

9.8 

888 

3-6 

20 

2-7 

4-2 

4710 

3-6 

0.001240 

2.6 

21 

i-7 

1  .0 

•3 

2840 

i  .  i 

22 

.... 

r 

•03 

6130 

•  5 

23 

.... 

o 

.... 

.0 

.0 

NUCLEATION     CONSTANTS     OF     CORONAS. 


59 


33.  The  violet  and  green  coronas.— The  object  of  the  series  of  experi- 
ments made  at  very  low  exhaustions  (dp  =  10)  and  compared  with  a  series 
for  high  exhaustions  (^  =  20.5)  was  an  estimation  of  the  importance 
of  the  time  effect  and  of  the  convective  effect  in  causing  loss  of  nuclei. 
If  the  latter  series  be  reduced  to  the  former  by  modifying  the  constants 
in  terms  of  pressure  and  temperature  the  coincidence  of  the  graphs  is 
complete,  as  shown  in  fig.  19.  This  indicates  that  the  method  of  reduc- 
tion is  reliable. 


600 


3000 


ZOOO 


1000 


4  6  8  tO  12  14-  16  18  ZO  2Z  Z4- 

FIG.   19. — Nucleation  n,  in  terms  of  the  apertures  of  coronas.    Results  in  tables 

1 8  and  19  compared. 

TABLE  21. — Violet  and  green  coronas,  d  and  s  values. 


Table 
and  ] 

3   16 

7-1 

Table 

18. 

Table 

19- 

Table 

2O. 

Color. 

a/»S  = 

17- 

»*.- 

10. 

*Pt—< 

Jo.  5. 

#•- 

17- 

Mean 
<fXio8 
and  s. 

dXio6. 

s. 

dXicP. 

s. 

dXio«. 

s. 

dXio*. 

S. 

Violet  (2)  ... 

190 
170 

17.0 

18-5 

190 
200 

17.2 

16  .0 

200 

15-8 

200 
1  80 

I6.3 

17     S 

191 
16.8 

2OO 

15.8 

Green  (2).  .  . 

220 
230 

14.4 
14.4 

220 
240 

14.4 
13-3 

230 
230 
2  "?O 

13.6 
14.1 

n  6 

230 

220 

13-8 
14.6 

228 
14.0 

Green  (3)  ... 

410 
370 

7-8 
8.6 

390 
42O 

8.1 
7-6 

4IO 
390 
4.IO 

7-9 

8.2 
7  .  0 

380 
4OO 

8.3 

8.0 

398 
8.1 

Green  (4)  ... 

1  Computed  with  n'=  o.  iggs*  and  y=  0.786,  the  latter  being  more  in  keeping  with  table  20. 


6o  CONDENSATION    OF   VAPOR   AS    INDUCED    BY    NUCLEI    AND    IONS. 

To  find,  however,  in  how  far  the  results  themselves  are  trustworthy, 
it  will  be  necessary  to  find  the  computed  values  in  the  different  series 
of  the  diameter  of  the  particles  producing  a  given  corona.  For  this 
purpose  the  violet  and  green  coronas  are  suitable.  There  are  three  of 
the  latter,  the  two  upper  being  very  brilliant.  In  the  former  report 
the  diameters  of  particles  were  estimated  as  d  =  0.000460  cm.  for  the 
middle  green  corona.  Ratios  of  4,  3,  and  2  were  usually  apparent, 
the  data  being  multiples  of  a  diameter  something  larger  than  d  =  o .  oooi  5 , 
the  corona  for  which  is  not  producible.  In  the  present  experiments 
the  values  of  d  and  5  for  the  green  coronas  are  given  in  table  2 1 . 

While  there  is  considerable  fluctuation,  the  data  approach  very  closely 
to  a  common  mean,  remembering  that  the  color  itself  necessarily  has 
a  certain  latitude  and  wide  differences  of  exhaustion  are  involved. 
The  ratio  2,  3,  4  of  diameters  of  fog  particles  is  not  as  well  suggested 
in  the  present  result  as  in  the  former,  while  the  absolute  sizes  themselves 
are  throughout  smaller.  It  is  nevertheless  convenient  to  retain  the 
ratio  for  the  division  of  coronas  into  successive  series.  If  these  may  be 
considered  as  beginning  with  deep  red  and  ending  with  violet  the  fol- 
lowing group  may  be  postulated: 

TABLE  22. — Showing  cycles. 

v,  (d =0.0001 1  cm.)      Uj>  d =0.00019  cm.      ^3.  d  =  0.00033  cm.  v4,  d  =  o. 00044  cm. 

g,  (                 13  cm.)      g2,                   23  cm.      g3)                   40  cm.  g4,                   52  cm. 

r,                     16  cm.        r2,                   32  cm.      r3,                   48  cm.  r4,                   64  cm. 

Only  the  red  and  crimson  of  the  first  series  are  certainly  observable 
with  the  above  apparatus.  Their  aperture  is  about  60°,  their  rings 
diffuse,  and  their  disk  filmy,  so  that  in  a  small  apparatus  they  would 
be  mistaken  for  clear  air.  The  second  series  is  producible  and  vivid 
throughout,  and  the  same  is  even  more  true  of  the  third.  The  fourth  is 
already  closely  packed,  while  the  fifth  and  subsequent  series  merge  into 
each  other  too  rapidly  for  separation. 

Series  3  and  4  were  obtained  in  great  number  in  my  work  with  at- 
mospheric nucleation.  Selecting  some  twenty  or  more  cases  the  mean 
ratio  i/ss  :  1/5-4  =  0.146  :  o.2o6=J3  :  d4.  Hence  the  ratio  of  3  :  4  is 
very  well  sustained.  The  goniometer  distance  from  the  fog  chamber 
was  nearly  a  meter  in  this  case.  In  the  present  experiments,  however, 
the  short  goniometer  distance  (D  =  ^o  cm.),  though  adapted  for  the 
best  seeing,  is  not  so  suitable  for  measuring  diameters.  Apart  from 
this,  the  former  experiments  wrere  made  with  plate-glass  apparatus. 
In  cylindrical  apparatus,  as  in  the  present  case,  there  must  have  been 
appreciable  refraction  due  to  differences  of  thickness.  Hence  it  is 
probable  that  the  series  i  is  actually  the  first  occurring,  although  the 
smallest  active  particles  (violet)  must  exceed  o.oooi  cm.  in  diameter. 
The  same  terminal  conditions  are  suggested  by  the  axial  colors  of  the 


NUCLEATION    CONSTANTS     OF    CORONAS. 


6l 


steam  jet.  It  seems  curious  that  the  diffraction  phenomenon  should 
begin  with  particles  of  the  order  of  three  times  the  wave-length  of  light. 
Using  the  method  of  contact  of  coronas  from  two  sources  described 
below,  the  ratio  of  diameters  of  the  first  four  series  is  much  more  nearly 
as  i,  2,  3,  4,  for  the  green  coronas  for  instance,  than  in  the  present 
experiments. 

34.  Insertion  of  new  values  for  rn. — The  values  of  m  used  in  the 
above  tables  were  throughout  obtained  from  the  earlier  experiments. 
As  the  relations  of  n  are  not  affected  and  as  m  does  not  influence  d  and  5 
(see  equations,  section  26)  the  latter  will  be  left  in  this  form.  The  nuclea- 
tion  n  varies  as  m.  Since  that  time,  however,  new  data  for  m  were 
investigated  compatibly  with  Chapter  II.  Inserting  these  in  tables  16 
and  17  and  agreeing  that  n  shall  hold  for  dp/p  =  o.2ig  and  20°,  io6  m  = 
3.2  must  be  replaced  by  io6  m  =  3.6.  In  table  20,  similarly,  for 
§p/p  =  o.  224  and  20°  C.,  io6  m  =  3  . 6  must  be  replaced  by  io6  m  =  3 .  7. 
These  results  have  been  compiled  in  table  23,  which  is  adapted  for 
practical  purposes.  The  results  are  nearly  coincident.  These  data  will 
be  used  in  preference  for  the  computation  of  nucleation. 

TABLE  23. — Values  of  s  and  n  referred  to  new  values  of  m. 


Table  16. 

Table  17. 

Table  20,  i. 

Table  20,  n. 

s. 

.Xior.. 

s. 

.XKrt 

s. 

.Xl«rt 

s. 

•»Xio-a. 

r'     27.8 

4490 

r'     30  .  2 

5710 

r'     30  .  o 

5460 

r'      27.0 

4163 

r'     25.8 

3620 

r'     27.6 

4400 

r'     27.2 

4233 

r'     24.8 

3223 

i'     23.7 

2708 

r'     25.4 

3420 

o      25.0 

3276 

r'     22.8 

2482 

r'     21.5 

2064 

r'     23.2 

2630 

o      23.0 

2545 

r      20.9 

1916 

c      19-5 

1558 

r      21.2 

2OIO 

O        21  .  I 

1957 

c      19.2 

H73 

v      17.8 

1176 

v      19.4 

1520 

ro    19.4 

v      17-5 

1123 

b      16.3 

886 

b'     17.7 

II4O 

v      16.3 

922 

bg  16.1 

861 

g      J4-5 

665 

B     15.8 

861 

b      15.0 

707 

g      14-6 

654 

g'     13-3 

500 

g      H-S 

649 

bg  13-8 

540 

gy  13-3 

495 

gy  12.  i 

373 

gy  13-3 

487 

yo  12.5 

409 

O         12.2 

372 

y  o  ii  .0 

278 

O         12.  I 

366 

ro    11.4 

310 

r      10.9 

276 

C         IO.O 

205 

ro    10.9 

270 

c      10.4 

233 

C         IO.O 

204 

P       8.9 

148 

P        9-8 

197 

P        9-4 

172 

9.0 

148 

g        7-9 

103 

g'       8.8 

140 

8-3 

126 

8.0 

107 

o        6.9 

69.6 

o        7.7 

97 

7-5 

88. 

7.0 

76.6 

6.0 

46-3 

br     6.8 

66 

6.5 

59-5 

6.1 

50.6 

5-2 

29.0 

5-9 

43 

5-7 

39-2 

5-4 

31.8 

4-3 

17.0 

27.6 

4-9 

24-5 

4-5 

19.0 

3-4 

8.1 

4.1 

15-3 

4.0 

13-9 

3-6 

10.  I 

2.O 

1.6 

3-2 

7-3 

3-2 

6-5 

2.6 

3-7 

I  .  ^ 

•4 

2.2 

2-3 

2.1 

1.9 

I.I 

•3 

.... 

1.6 

.8 

1-5 

.6 

•5 

•03 

IO9W  = 

3-6 

.... 

3-6 

3-7 

.... 

3-7 

.... 

dp/p= 

d  = 

.219 
.oigow-1/3 

.219 
.oigow"1/3 



.224 

.OI92W"1/3 

.224 

.OI92W-1/3 

s  = 

.  i68rtV3 



.  i68«V3 

.  i67»V 

.... 

.  I67W1/3 

.... 

62 


CONDENSATION    OF   VAPOR   AS    INDUCED    BY    NUCLEI    AND    IONS 


To  reduce  the  other  tables  to  the  same  standards  (remembering  that 
n  varies  as  m,  while  d  and  5  are  independent  of  it),  is  not  necessary  for 
the  present  comparisons.  In  table  18,  however,  10  w6  =  2.i  should  be 
replaced  by  io6  m  =  2  .3,  where  dp/p  =  o.  133.  In  table  19,  dpjp  —  0.2 73, 
io6  m  =  4.i  is  to  be  replaced  by  io8  ^  =  4.3.  In  all  cases  the  initial 
nucleations  are  thus  increased.  The  new  values  for  m  are  referred  to 
20°  C.  and  the  temperature  coefficient  is  about  2  per  cent  per  degree. 

35.  Wilson's*  data  and  conclusions. — The  following  table  (24)  con- 
tains Wilson's  exhaustions  (v^/v)  at  18°  to  19°  C.  and  the  correspond- 
ing disk  colors  as  I  interpret  them.  It  also  contains  the  equivalent 
relative  drop  of  pressure  dp/p  used  above.  From  these  and  the  colors, 
the  diameters  of  fog  particles  (d)  may  be  estimated,  provided  the  series 
in  which  these  colors  lie  is  known ;  hence  d,A  2  refers  to  the  probable  case 
of  the  occurrence  of  the  third  and  second  series,  d2 1  to  the  very  im- 
probable case  of  the  occurrence  of  the  second  and  first  series.  Hence 
if  the  values  m  be  found  for  the  corresponding  temperature  and  ex- 
pansions (dp Ip)  the  nucleations  n32  and  w21  respectively  follow.  Wilson 
gives  but  a  single  series  between  green  coronas.  There  are  two  such 
series  and  three  definite  green  coronas  producible,  and  I  shall  assume 
that  the  very  vivid  upper  one  is  meant.  The  first  series  is  not  pro- 
ducible by  any  means  known  to  me,  except  in  the  lower  red  coronas. 
Hence  I  ignore  w2>1  and  take  w3>2,  in  which  case  the  data  are  distributed 
similarly  to  my  own,  so  far  as  the  slope  of  the  curves  is  concerned. 

24. — Estimation  of  the  nucleation  and  size  of  nuclei  corresponding  to  Wilson's 
colors  for  wet  dust-free  air.    Temp.  18°  to  19°  C. 


From  d. 

From  color. 

Vi/V. 

io3X 
dp/p. 

Disk 
color. 

d3,2Xio5. 

d2>l  X  io5. 

w3,2Xio-3. 

n2)l  X  io-3. 

«3)2Xio-3. 

n2>1  X  io~3. 

.410 

384 

g 

40 

23 

1  60 

870 

190 

870 

.410 

384 

g 

.... 

.... 

.... 

.413 

386 

g 

.416 

388 

bg 

.418 

389 

b 

.... 

.419 

390 

V 

33 

19 

290 

1460 

'265 

1500 

.420 

390 

V 

.420 

390 

r  p 

.426 

394 

r 

32 

16               325 

2650 

320 

2150 

.429 

396 

rg 

....              .... 

•  436 

400 

y  w 

.448 

401 

w 

....              .... 

.469 

418 

gw 

23 

12                     910 

6500 

910 

7000 

•373 

360 

Fog  limit. 

•3i 

3T7 

-fions,  condensation  limit. 

•25 

270 

—  ions,  condensation  limit. 

*Phil.  Trans.  Roy.  Soc.,  vol.  189,  p.  265,  1897.    Cf.  p.  285. 


NUCLEATION     CONSTANTS     OF    CORONAS.  63 

There  is  another  way  in  which  the  estimate  in  question  may  be  made. 
Let  the  nucleations  corresponding  to  the  colors  be  taken  and  reduction 
made  for  the  different  drops  of  pressure  in  question.  This  is  merely 
a  corroboration  of  the  method  of  computation.  The  coincidence  is  as 
close  as  may  be  expected,  as  the  methods  of  approach  are  widely  differ- 
ent and  the  nucleation  varies  as  the  cube  of  the  inverse  diameter. 

Wilson's  views  of  the  nature  of  the  phenomena  are  quite  different 
and  lead  to  enormous  nucleation,  even  as  compared  with  the  improbable 
n21.  He  says  (loc.  cit.,  p.  301): 

When  all  diffraction  colors  disappear  and  the  fog  appears  white  from  all  points  of 
view,  as  it  does  when  [the  expansion]  v2/v1  amounts  to  about  i .  44,  we  can  not  be  far 
wrong  in  assuming  that  the  diameter  of  the  drops  does  not  exceed  one  wave-length  in 
the  brightest  part  of  the  spectrum,  that  is,  about  5Xio~5  cm.  That  the  absence  of 
color  is  not  due  to  the  inequality  of  the  drops  is  evident  from  the  fact  that  the  colors 
are  at  their  brightest  when  1^2/^1  is  only  slightly  less  than  i .  44  and  from  the  perfect 
regularity  of  the  color  changes  up  to  this  point. 

Taking  the  diameter  of  the  drops  as  5Xio~5  cm.,  we  obtain  for  the  volume  of  each 
drop  about  6  X  io~14  c.  cm.,  or  its  mass  is  6  X  io~14  gram. 

Now,  we  have  seen  that  when  the  expansion  is  such  as  produces  the  sensitive  tint 
(when  v2/'Vi==  I  -42)>  the  quantity  of  water  which  separates  out  is  about  7.6X10"' 
gram  in  each  cubic  centimeter.  With  greater  expansions  rather  more  must  separate 
out.  We  therefore  obtain  as  an  inferior  limit  the  number  of  drops,  when  lyfy  =  i .  44, 
7 . 6  X  io8/6  X  io~14=  io8  per  cubic  centimeter. 

In  my  data  the  smallest  green  corona  corresponds  to  a  diameter  of 
particles  of  about  d4  =  0.0005  2  cm.,  the  next  to  0/3  =  0.00040  cm.,  the 
next  to  d4  =  0.0002 3,  the  first  (which  I  have  not  been  able  to  produce 
by  any  means  whatever,  however  large  the  nuclei)  should  correspond 
to  ^  =  0.00013  cm.,  and  even  this  calls  for  particles  nearly  three  times 
as  large  as  Wilson's  estimate  (0.00005  cm.).  In  a  small  tube  but  2  cm. 
in  diameter,  like  Wilson's  test-tube  apparatus,  it  is  improbable  that  the 
d2  green  corona,  which  is  about  27°  in  angular  diameter,  could  look 
otherwise  than  greenish  white,  whereas  the  filmy  disk  of  the  large 
crimson  coronas  (the  largest  producible,  6^  =  0.00016,  with  an  angular 
diameter  of  about  39°)  would  be  mistaken  for  colorless.  I  shall  venture 
to  believe,  therefore,  that  Wilson's  large  greenish-white  coronas  corre- 
sponded to  about  o .  9  X  io6  rather  than  to  io8  nuclei  per  cubic  centimeter, 
and  that  the  maximum  nucleation  would  not  exceed  io7  even  if  colors  of 
the  unapproachable  first  order  were  produced. 

36.  Longer  intervals  between  observations.  Conclusion. — Finally,  experi- 
ments were  made  with  longer  intervals  of  time,  2  minutes  and  3  minutes, 
between  the  observations.  The  object  in  view  was  the  avoidance  of 
distortion  of  the  higher  coronas  due  to  the  absence  of  homogeneous  nucle- 
ated wet  air  in  the  fog  chamber.  But  the  longer  intervals  did  not  improve 
the  coronas  and  the  data  were  for  this  reason  discarded. 


64          CONDENSATION    OF   VAPOR   AS    INDUCED    BY   NUCLEI    AND   IONS. 

Using  the  method  of  successive  equal  exhaustions  for  standardization 
and  a  single  spot  of  light  as  the  source  of  diffractions,  the  coronas  of 
cloudy  condensation  were  overhauled  in  the  above  chapter  with  special 
reference  to  the  use  of  an  efficient  plug-cock  fog  chamber.  The  ratio 
of  the  section  of  the  exhaust  to  the  section  of  the  fog  chamber  was  about 
one  to  six.  The  useful  equations  are  summarized.  The  chief  difficulty 
encountered  is  the  extreme  sensitiveness  of  the  coronas  produced  to 
any  lack  of  homogeneity  in  the  nucleation  of  the  air. 

Given  types  of  coronas,  like  the  green  pattern,  for  instance,  seem  to 
recur  for  the  ratios  of  4,  3,  2,  i  in  the  diameters  of  the  fog  particles. 
The  results  as  a  whole  show  fairly  good  agreement  with  the  earlier 
results  below  the  middle  green-blue-purple  corona,  but  above  this  the 
divergence  of  values  has  not  been  much  improved.  In  the  definite 
region  specified,  corrections  need  be  made  for  subsidence  only.  The 
fiducial  value  of  the  nucleations  of  normal  coronas  has  been  accepted  as 
heretofore. 

It  does  not  seem  probable  that  fog  particles  as  small  as  o.oooi  cm. 
are  ever  measurably  encountered  in  the  fog  chamber.  This  is  larger 
than  Wilson's  estimate  made  in  terms  of  the  wave-length  of  light;  but 
detailed  comparisons  are  unsatisfactory,  because  of  the  difficulty  of 
identifying  his  colors  as  to  their  place  in  the  observed  cycles  of  colors. 


NUCLEATION    CONSTANTS     OF    CORONAS.  65 

DISTRIBUTION  OF  VAPOR  NUCLEI  AND  OF  IONS  IN  DUST-FREE  WET 
AIR.     CONDENSATION  AND  FOG  LIMITS. 

37.  Introductory.  —  It  will,  in  the  first  place,  be  desirable  to  gather  cer- 
tain of  the  older  data  together  for  the  comparison  of  fog  limits.     There 
is,  in  fact,  quite  a  serious  discrepancy  between  Mr.  Wilson's  results  and 
mine  when  reduced  to  the  same  scale.     Mr.  Wilson's  supersaturations 
for  negative  ions  and  cloud  are  distinctly  higher,  which  seems  to  mean 
nothing  less  than  that  my  fog  chamber,  instead  of  being  inferior,  is  in 
these  regions  superior  to  his  own.     Thus,  in  moderately  ionized  air  my 
condensations  begin  at  a  drop  of  about  18.5  cm.  from  76  cm.  as  com- 
pared with  20.5  in  Wilson's  apparatus;   similarly,  my  fogs  begin  at  the 
drop  20.3,  Wilson's  at  27.7.     Furthermore,  at  low  ionization  even  the 
vapor  nuclei  of  dust-free  wet  air  become  efficient  in  the  presence  of  ions. 
It  seems  impossible,  therefore,  that  any  positive  ions  should  fail  of  capture. 

38.  Notation.  —  The  whole  case  may  best  be  represented  graphically, 
but  the  tables  will  also  be  given.     In  my  apparatus,  however,  the  adia- 
batic  volume  expansion  vl/v  is  a  troublesome  datum  to  compute  accu- 
rately;  it  appears  as 


where  p  and  p'  are  the  pressures  in  the  fog  and  vacuum  chambers  before 
exhaustion,  p3  their  common  pressure  when  in  communication  after 
exhaustion,  always  at  the  same  temperature.  The  volume  ratios  of  the 
chambers  is  [v/V]=  0.064;  the  TT'S  denote  the  different  vapor  pressures 
and  k  and  c  the  specific  heats.  With  a  large  vacuum  chamber  the 
approximation 


may  be  used,  so  that  if  dp=p  —  p3,  the  convenient  variable  for  the  com- 
parison of  exhaustions  is  the  relative  drop  dp/p3.  This  is  used  in  the 
diagram  with  the  approximate  equivalent  of  the  volume  expansion  v1/v. 
(Cf.  Chapter  I.) 

39.  Data.  —  In  table  25  results  are  given  for  the  conditions  observed 
near  the  fog  limits  of  dust-free  air,  and  of  dust-free  air  weakly  ionized 
by  the  beta  and  gamma  rays  (coming  from  a  closed  tube  containing 
radium  placed  on  the  outside  of  the  fog  chamber)  and  strongly  ionized  by 
the  X-rays  (at  a  distance  D  from  the  fog  chamber)  .  The  data  for  ionized 
air  are  nearly  coincident,  but  dust-free  air  requires  higher  supersatura- 
tion.  The  notation  is  as  above,  p,  p—dp'  being  the  pressures  of  the  fog 
and  vacuum  chambers  before,  p—8p3  the  common  pressure  after  ex- 
haustion. The  relative  drop  in  pressure  is  x,  the  angular  diameter  of  the 
coronas  5/30,  the  number  of  nuclei  per  cubic  centimeter  n,  the  volume 


66 


CONDENSATION    OF   VAPOR   AS    INDUCED   BY    NUCLEI    AND    IONS. 


TABLE  25. — Fog  limits  of  non-energized  air,  of  air  energized  by  weak  radium,  and  by 
intense  X-rays.    £>  =  35  cm.,  anticathode  to  axis  of  fog  chamber. 


w. 

*. 

s. 

M. 

nX  io~3. 

vjv. 

Bar.  76. 

2  cm.;   t 

emp.  26° 

to  28°  C. 

Radium            .  . 

21     I 

IQ    7 

4.   "> 

O    2^Q 

22 

2  77 

21.3 

I9.8 

4-2 

.260 

18 

•238 

20.0 

18.4 

*r 

.242 

O.  2 

.217 

20.2 

18.9 

i  .5 

.248 

0.6 

.224 

Air        

2  o         <7 

21  .  5 

I  .  7 

.282 

I    2 

26  s 

22.8 

(21.  I) 

I  .2 

.277 

0.4 

•259 

21  .9 

20.3 

lr 

.266 

0.2 

.246 

21.3 

19.6 

0.0 

•257 

0.0 

•234 

X-rays  

2O.4. 

19.4 

4-  I 

17 

.  272 

18.9 

17.2 

0.0 

.226 

0.0 

.199 

19.6 

18.0 

0.0 

•236 

0.0 

.  211 

20.0 

18.4 

1.8 

.242 

1-3 

.217 

20.4 

19.2 

3-8 

.252 

.228 

Bar.  7 

5.8  cm.; 

temp.  i< 

3.6°C. 

Radiation. 

dps- 

s. 

dps/p* 

wXio-3. 

vjv. 

n^  X  io-3. 

Radium  

20  6 

6    2 

O    272 

60 

2  eo 

18.6 

T 

•245 

0.2 

.221 

0.2 

X-rays,  D  =  1  50  cm  .  .  . 

18.6 

r 

•245 

0.2 

.221 

0.2 

X-rays,  with  radium  .  . 

18.6 

2r 

•245 

0.2 

.221 

0.2 

X-ray,  D  =  ^o  cm.  and 
radium,  D  =  50  cm  .  . 

1    18.4 
I    18.7 

2r 

•243 
•247 

O.  2 
1-5 

.218 
•223 

0.2 
1-3 

Radium  

18  7 

r 

24.7 

O    2 

227 

O    2 

Do  

21    6 

37   O 

28=; 

80 

260 

7     ^ 

X-rays,  D  —  50  

2O    7 

4Q    S 

277 

2IO 

2  ^4 

176 

No  corona  visible;  scattered  rain.         2  Coronas  gradually  increasing.         3  w  y  .         4  w  c. 


26.  —  Dust-free  wet  air  energized  by  weak  radium  acting  from 
Bar.  75  .  8  cm.  ;   temp.  27°  C.    Wet  glass  walls. 


*y. 

*/v 

J. 

*PJP- 

nXio-3. 

*!/»• 

25.6 

24.1 

4-3 

0.318 

23 

.312 

24.6 

23.0 

3-9 

•304 

17 

•293 

23.2 

21.8 

3-9 

.288 

16 

•273 

21.8 

20.5 

3-8 

.271 

H 

.252 

21.  I 

19.8 

2-5 

.261 

3-6 

•239 

20.2 

18.8 

r 

.248 

0.2 

.224 

20.1 

18.8 

0 

.248 

0.0 

.224 

21.9 

20.6 

3-8 

.272 

H 

•253 

24.0 

22.3 

3-7 

.294 

14 

.280 

25-5 

23-9 

3-8 

•3i5 

17 

.308 

27-5 

25.7 

4.6 

•339 

28 

•342 

29.  2 

27.5 

5-5 

.363 

50 

•377 

31-2 

29.0 

x7-5 

.383 

133 

.408 

=        cm. 


NUCLEATION    CONSTANTS    OF    CORONAS. 


67 


expansion  on  exhaustion  vjv.  Tables  26  and  27  contain  corresponding 
results  for  air  energized  by  the  weak  radium  at  a  distance  £>  =  35  or  40 
cm.  from  the  fog  chamber.  The  difference  observed  in  the  curves  of 
successive  identical  experiments  was  found  to  be  referable  to  the  wet 
or  dry  condition  of  the  inside  of  the  glass  walls  of  the  fog  chamber. 
Freshly  wet  walls  are  apparently  essential. 

TABUS  27. — Dust-free  wet  air  energized  by  weak  radium  acting  from  0  =  40  cm. 
Supplementary  data.    Bar.  76.2  cm.;  temp.  24°  C.    Dry  glass  walls. 


9?. 

#•• 

s. 

9pt/p. 

wXio-3. 

Vi/V. 

n^  X  io~3. 

'   25.6 

24.0 

3-9 

0.315 

17 

-308 

16 

26.1 

24-5 

3-9 

.322 

17 

.318 

16 

26.7 

25.0 

3-9 

•327 

J7 

•  325 

16 

27.2 

25-5 

3-9 

•334 

18 

•335 

17 

28.1 

26.5 

4.2 

•346 

23 

•352 

21 

28.9 

27.2 

5-2 

•356 

4i 

.365 

39 

30.1 

28.3 

6-5 

•371 

86 

•389 

81 

28.6 

27.1 

5-o 

•354 

37 

•364 

35 

28.5 

26.8 

4-9 

•  350 

34 

•357 

32 

21.8 

20.6 

3-6 

.270 

12 

.250 

ii 

21  .  I 

19.9 

2.0 

.261 

2 

•239 

2 

20.6 

19.4 

r  i  .0 

•  255 

O.  2 

•  232 

O.  2 

20.6 

19.6 

r  i  .0 

•257 

O.  2 

•234 

O.  2 

Repeated.  Glass  vessel  clean  and  wet 

27.2 

25-7 

4-5 

0-337 

27 

•339 

26 

28.3 

26.7 

5-o 

•349 

36 

•356 

34 

26.4 

24.7 

4.2 

•323 

21 

•319 

20 

25-7 

24.0 

4.2 

.315 

21 

.308 

20 

24-5 

23.2 

4.0 

•304 

18 

•293 

17 

24.0 

22.3 

3-8 

.292 

15 

.278 

16 

22.  O 

20.  6 

3-6 

.270 

12 

.250 

12 

21  .O 

19.9 

2.4 

.261 

3 

•239 

3 

In  table  28  the  ionization  is  slightly  intensified  by  affixing  the  radium 
tube  to  the  outside  of  the  walls  of  the  fog  chamber.  In  table  2  9  there  is 
further  intensification,  obtained  by  acting  upon  the  fog  chamber  with 
the  X-rays  at  d  =  $o  cm. 

28. — Dust-free  wet  air  ionized  by  weak  radium  (10  mg.  10,000  X)  on  glass  fog 
chamber.     Bar.  74.9  cm.,  75.0  cm.;   temp.  17.7°  C. 


tyf 

s. 

8PJP- 

wXio-3. 

Vi/V. 

*P* 

s. 

*P»/P- 

nX  io-3. 

vi/v- 

20.5 

6-5 

0.273 

69 

•254 

24.1 

6-9 

0.321 

92 

.316 

19.4 

3-4 

•  259 

10 

•237 

26.0 

6.8 

•347 

93 

•352 

17.9 

.0 

•  239 

O 

.214 

29.4 

6.9 

•  392 

1  06 

•423 

18.3 

r  i.o 

.244 

O.2 

.219 

32.5 

6.9 

•433 

112 

.496 

19.9 
22.3 

5-5 
6-9 

.265 
•297 

40 

86 

.244 
.284 

39-4 
42.8 

Diffuse 
Diffuse 

•525 
•571 



•695 
.823 

Fog  limit  below  ^  =  0.756  at  18°,  equivalent  to  ^=1.22,  equivalent  to  a  drop 
(adiabatically)  of  dp=  18.6  cm.  (about  )  at  76  cm,,  2  cm.  below  Wilson's  ^  =  20.5  cm. 


68 


CONDENSATION    OF    VAPOR   AS    INDUCED   BY    NUCLEI    AND    IONS. 


TABLE  29. — Dust-free  wet  air  ionized  by  X-rays  at  £>  =  5o  cm.     Bar.  75.9  cm.; 

temp.  21.3°  C. 


2ZQ 


i 

9P* 

s. 

8P*/P> 

wXio~3. 

vjv. 

9p» 

S. 

8pjp. 

rcXio-3. 

•oj-v. 

I 

18.4 

r 

o.  242 

O.  2 

1.  218 

20.2 

^.I      0.266 

125 

1.245 

18.9 

2-4 

.249 

3-3     1-225 

19.4 

5-o       .255 

29 

1.232 

19.6 

5-2 

.258 

32       ;  1.236        19.0           i  .9       .250             i  .5 

i  .  226 

1             1; 

1                  ! 

wp  corona. 


.Z7       .28        .29       .30        .3\1        .32       JB      „  .£/       J'J"       .JP        .«?7        .38        .J9 


FIG.  20. — Nuclealion  n  of  dust-free  air  and  of  ionized  air  in  terms  of  relative  adiabatic 
drop  in  pressure  dp/p  and  of  volume  expansion  vj-v.  Enlarged  scale  for  n.  Region 
for  ions. 

FIG.  21. — Nucleation  n  in  terms  of  relative  adiabatic  drop  of  pressure  Sp/p,  and  of 
volume  expansion  vt/v  for  dust-free  air  not  energized,  and  for  dust-free  air  acted  on 
by  the  beta  and  gamma  rays  of  radium  and  by  the  X-rays  from  different  distances  D. 
W  refers  to  C.  T.  R.  Wilson's  condensation  and  fog  limits,  B  to  my  own;  T  shows 
J.  J.  Thomson's  results  referred  to  scale  of  the  diagram.  Several  older  series,  V  to  X, 
are  given  for  dust-free  air. 

40.  Graphs.  Dust=free  air. — The  charts  (figs.  20,  21,  and  22)  con- 
tain a  number  of  curves  showing  the  nucleation  in  different  scales  (com- 
puted from  the  angular  diameter  of  coronas)  in  terms  of  the  exhaustion. 
In  figs.  20  and  21  typical  cases  are  given,  in  their  lower  parts  only.  Fig. 
22  contains  full  curves  on  a  smaller  scale.  Thus  the  curve  for  the  vapor 
nuclei  of  dust-free  air  begins  appreciably  below  dp/p  =  o .  26  (v1/v  =  i .  24, 


NUCLEATION     CONSTANTS    OF    CORONAS. 


K>    ft 

'  8. 


? 


1 

CTcn 


.«  3 


3" 
If 

O   o' 


70          CONDENSATION    OF   VAPOR   AS    INDUCED    BY    NUCLEI    AND    IONS. 

adiabatic  drop  from  76  cm.,  19.8  cm.),  but  it  hugs  the  axis  until  about 
0.33,  after  which  it  sweeps  upward  far  beyond  the  chart  into  the  hun- 
dred-thousands. The  position  of  Wilson's  negative  ions  and  positive 
ions  is  indicated  at  0.27  and  above  0.31.  Wilson's  fog  point  would  lie 
at  o .  36  in  the  chart  and  there  would  be  an  air  curve  to  the  right  beyond. 
Series  III  to  X  are  taken  from  my  earlier  report  (Carnegie  Institution 
of  Washington  Publication  No.  62,  1907,  p.  67).  The  serial  number  is 
marked  on  the  curve. 

41.  Weak  radiation. — If  a  weak  ionizer  (radium  io,oooX,  100  mg., 
sealed  in  an  aluminum  tube)  is  placed  at  D  =  4o  cm.  from  the  glass  fog 
chamber,  the  air  curve  rises  slightly  above  dp/p  =  o.2$,  becomes  nearly 
constant  slightly  above  0.27  until  above  0.35,  after  which  it  also  begins  to 
sweep  with  great  rapidity  into  the  hundred-thousands  of  nuclei.    That  is, 
at  weak  ionization  the  vapor  nuclei  of  dust-free  wet  air  become  efficient 
in  the  presence  of  ions.     There  are  but  two  steps  in  the  curve,  the  initial 
one  scarcely  leaving  the  axis,  the  other  at  about  n  =  15,000  to  20,000. 

42.  Moderate  radiation. — Let  the  radium  tube  be  attached  to  the  outer 
surface  of  the  fog  chamber.    The  curve  which  is  obtained  begins  appre- 
ciably slightly  above  dp/p  =  0.24  (ujv  =  1.21,  adiabatic  drop  from  76  cm. 
about  18.4  cm.),  but  it  scarcely  rises  until  above  0.25.    From  this  point 
it  also  sweeps  upward  but  can  not  get  much  above  70,000  to  80,000 
nuclei  per  cubic  centimeter,  which  condition  is  reached  at  about  0.28. 
To  make  this  curve  rise  into  the  hundred-thousands,  i.  e.,  to  make  the 
vapor  nuclei  of  dust-free  wet  air  efficient  in  the  presence  of  the  ions, 
the  exhaustion  must  be  carried  to  about  o.  50,  much  beyond  the  lateral 
limits  of  the  diagram;   but  the  fog  is  then  intense  and  without  coronas. 
Again  there  are  but  two  steps,  one  very  near  the  axis  not  appreciably 
influenced  by  the  greater  ionization  and  the  other  above  n  =  70,000. 
Persistent  nuclei  are  not  produced,  however  long  the  exposure. 

43.  Strong  radiation. — If  an  ordinary  X-ray  bulb    (4-inch  spark)    is 
placed  at  a  distance  of  about  50  centimeters  from  the  fog  chamber,  the 
condensation  produced  begins  appreciably  somewhat  below  0.24  (vjv  = 
i  .21',  adiabatic  drop  from  76  cm.  about  18  cm.) ;  but  the  graph  scarcely 
rises  until  nearly  0.25,  when  the  upward  sweep  into  the  hundred-thou- 
sands begins.     Exposure  of  a  few  seconds  produces  fleeting  nuclei  only ; 
exposure  of  one  or  more  minutes  produces  persistent  nuclei.     In  spite 
of  intense  ionization,  the  first  step  near  the  axis  has  scarcely  risen;  the 
other  is  indefinitely  high  beyond  the  reach  of  coronas. 

44.  Other  nucleations. — I  have  ventured  to  place  the  data  of  J.  J. 
Thomson  (Phil.  Mag.,  vol.   v,   1903,  p.   349)   at  T  in  the  same  chart. 
They  must  be  interpreted,  however,  relatively  to  Wilson's  points  (nega- 


NUCLEATION    CONSTANTS    OF    CORONAS.  71 

live  ions  v1/v  =  i  .25,  positive  ions  i  .31,  cloud  i  .38).  In  relation  to  the 
other  curves  of  the  chart  Thomson's  graph  must  be  shifted  bodily  toward 
the  left  until  the  lower  and  upper  steps  of  the  curve  correspond  with  the 
other  cases.  In  none  of  the  experiments  made  with  my  apparatus  does 
the  initial  step  (which  should  correspond  to  the  branch  for  negative 
ions)  rise  much  above  the  horizontal  axis,  no  matter  how  intense  the 
ionization.  This  rise  begins  at  about  0.25  in  the  chart  and  continues 
thereafter  in  a  way  to  correspond  with  the  ionization.  The  diagram 
also  shows  J.  J.  Thomson's  second  group  of  experiments,  in  which  the 
initial  step  (v^/v  <  i .  33)  lies  at  an  average  height  of  n  =  8$  X  io3  and  the 
second  step  at  an  average  height  about  twice  as  large. 

Fig.  22,  wrhich  contains  most  of  the  earlier  results  reduced  to  the 
present  scale,  shows  the  variation  of  nucleation  obtainable  at  different 
times  to  which  reference  has  already  been  made.  The  high  position  of 
the  X-ray  curve  is  particularly  noticeable.  All  data  except  C.  T.  R. 
Wilson's  are  given  as  if  the  coronas  had  been  observed  at  27°,  for  which 
case  the  least  amount  of  reduction  was  needed.  The  Wilson  line  should 
therefore  be  depressed  about  8X2=16  per  cent  in  nucleation  to  be 
comparable  with  the  others. 

45.  Temperature  effects. — It  was  demonstrated  in  Chapter  II  that 
the  vapor  nucleation  of  dust-free  air  varies  in  marked  degree  with  tem- 
perature, if  the  relative  drop  in  pressure  be  computed  as  x=(dp3 — [n  — 
nJ)/(P — 7r)-  Computed  relatively  to  dp3/p,  there  is  a  much  more  mod- 
erate variation  with  temperature  outstanding,  suggesting  that  the  appar- 
ent variation  may  be  associated  with  the  occurrence  of  the  vapor  density 
TT  in  x.  To  throw  light  upon  this  subject  from  a  different  point  of  view, 
the  condensation  limits  of  dust-free  air  and  of  ionized  air  were  determined 
at  temperatures  between  13°  and  30°  and  table  30  contains  the  results. 
The  notation  being  as  above,  it  is  only  necessary  to  refer  to  the  final 
column  for  dpa/p  and  the  volume  expansion  vl/v=(p/[p — <^3])1/T, 
computed  therefrom. 

The  results  of  table  30  being  summarized  by  giving  expansions  corre- 
sponding to  the  fog  limits  both  for  [v1/v]  =  (i  —  x)l/v  and  vjv=(i- 
dp3/PYly,  show  clearly  that  vjv,  computed  from  dp3/p,  is  independent 
of  temperature,  whereas  the  other  datum  [vjv]  varies  with  temperature 
in  a  way  referable  to  the  values  of  TC  involved.  It  follows  that  the  fog 
limits  are  not  changed  by  temperature  in  a  way  found  by  the  nucleation 
itself  in  Chapter  II.  The  mean  fog  limit  for  dust-free  air  vjv  =  i  .252 
agrees  with  Wilson's  data.  The  fog  limit  for  ionized  air  is,  however, 
decidedly  below  this,  and  thus  below  Wilson's  value.  Finally,  [vjv]  is 
always  less  than  vjv  and  under  ordinary  temperatures  from  i  to  2  per 
cent  less. 


CONDENSATION    OP   VAPOR   AS    INDUCED    BY    NUCLEI    AND    IONS. 


TABLE  30. — Temperature  comparisons.     Radium  on  top  of  fog  chamber.     D  =  o. 


Tem- 

Tem- 

pera- 

. 

pera- 

. 

dp'. 

dp,. 

S. 

nXio  \ 

ture  and 
barom- 

$PS/P- 

8P'. 

#.- 

s. 

ttXio   «. 

ture  and 
barom- 

dp,/ p. 

eter. 

eter. 

Ions  due  to  radium. 

Vapor  nuclei.     Wet  dust-free  air. 

22.6 

21.5 
20.3 

21.6 
20.  I 
I9.O 

6.8 
o.o 

80 

O.  I 

14.0° 
76.  i  cm. 

1.226 
0.250 



25-6 
24.6 

4-6 
3-6 

28.6 
13-9 

30.0° 
75.  7  cm. 

22    7 

-2      6 

13  .  i 

20.  6 

19.5 

2.  I 

2.0 

22.5 

21.5 
20.  i 

21-5 
2O.  I 

I8.4 

18.6 

6.6 
5-0 

74 
29 

I.O 
O.  I 

30.0° 

75  .7  cm. 

I  .  222 
[0.246 
1   0.243 

20.  o 

21  .  I 
2O.  I 
20.3 
18.7 

2-5 

o.o 
o.o 

3-8 
o.o 

O.  I 
0.0 

'  '  '  'o 

1.247 

Jo.  265 

\  0.268 

18  4. 

o  o 

o  o 

21  .9 

20.3:     o.o 

0.0 

76.8  cm. 

22-9 

21.6       0.0 

0.0 

18.6 
19.2 

20.0 

19.4 

17.5 
18.0 

18.8 

3-2 

0.0 
0.0 

0.5 

7-5 

0.0 

o.o 

O.  I 

13  '-2° 

76.8  cm. 

I  .220 
0.245 

-'3-8 
23-3 

22.8 

22.  I  >I.O 

21.9  >  i  .0 

21-5       0.5 

0.2 
O.  2 
O.  I 

::;; 

i  .263 
[0.285 
\  0.280 

Vapor  nuclei. 

Ions  due  to  radium. 

21.8 

20.4 

0.5 

O.  I 

14.0° 

1.247 

19.2 

18.1 

o.o 

0.0 

14.0° 

1.226 

22.4 

21  .  I 

I.O 

0.2 

76.0  cm. 

f  0.268 

19.8 

18.6 

o.o 

O.O 

76      cm. 

;  0.245 

20.3 

o.o 

0.0 



\  0.267 

20.  6 

19.4 

strong 

O.  I 

10.255 

SUMMARY    OF    RESULTS. 


Ionized  air. 

Dust-free  air. 

v\h> 

-vj-v. 

Differ- 
ence. 

vjv. 

vjv. 

Differ- 
ence. 

14° 
30 
13 
H 

Mean.  . 

i  .  226 
i  .  220 
i  .  220 
i  .  226 

i  .  214 
i  .  196 

I.  212 
I  .  214 

O.OI2 
.24 
.08 
.  12 

1.247 
1.263 
1.247 

I  .  222 
1.252 
1-257 

0.025 
.on 
.010 

1.223 



.... 

1.252 

46.  New  investigations. — In  tables  3i,32,and33  data  were  investigated 
for  X-rays  of  different  strengths  and  for  dust-free  air.  In  the  latter 
case  the  coincidence  of  data  is  not  as  close  as  was  anticipated,  different 
apparatus  showing  a  somewhat  different  behavior.  The  results  are  all 
given  in  fig.  23.  The  drop  in  the  upper  X-ray  curve  is  probably  due  to  a 
breakdown  in  the  X-ray  bulb,  as  it  is  not  sustained  by  the  other  curves. 

Fig.  23  also  contains  Wilson's  series,  under  the  supposition  that  the 
coronas  begin  with  the  green  of  the  third  and  end  with  the  green  of  the 
second  series.  In  such  a  case  the  present  results  lie  in  a  region  of  lower 
supersaturation  than  Wilson's.  The  slopes  throughout  are  similar.  If 
Wilson's  colors  are  of  the  second  and  first  series,  the  green  alone  will 
appear  in  the  diagram,  the  other  nucleations  being  too  high.  In  such  a 
case  Wilson's  line  will  intersect  the  graphs  of  the  present  paper,  as  shown 
by  the  graphs  of  the  point  g2l. 


NUCLEATION    CONSTANTS    OF    CORONAS. 


73 


74 


CONDENSATION    OF   VAPOR   AS    INDUCED   BY   NUCLEI    AND   IONS. 


TABLE  31. — Weak  X-rays.     App.  II.     Bar.  75.68    cm.,  75.86  cm 75.8  cm; 

temp.  25.o°C.    February  18,  1907. 


Cor- 

Cor- 

dp. 

s. 

Cor. 

dp3/p. 

wXio~3. 

rected 

9p. 

s. 

Cor. 

dpa/p. 

wXio-3. 

rected 

wXio-3. 

wXio-3. 

(1)17.6 

0 

0.232 

o 

o 

(034-6 

II  .0 

0-457 

594 

677 

18.6 

2.5 

cor 

•  245 

3 

4 

II  .  I 

y 

.410 

562 

638 

19-5 

5-2 

0 

•  257 

32 

35 

2S'.l 

11.4 

y 

•376 

529 

598 

19.7 

7.0 

c 

.260 

83 

92 

25-3 

n-5 

y 

•334 

490 

549 

19.9 

7-o 

o 

.263 

90 

100 

23.0 

II.  0 

o 

•303 

403 

450 

20.  o 

7-4 

gy 

.264 

97 

108 

20.8 

9-5 

p 

.274 

211 

234 

20.5 

9.2 

c 

.271 

191 

212 

19.1 

3-9 

cor 

.252 

I4.6 

16.1 

21.8 

9-3 

c 

.287 

207 

230 

19.9 

7.0 

0 

•  263 

84 

93 

25.5 

ii  .0 

o 

.336 

467 

523 

20.  o 

7-3 

g 

.  264 

94 

104 

30.0 

ii  .0 

.  .  .  . 

•  396 

550 

622 

20.4 

8-7 

P 

.  269 

155 

172 

TABLE  32. — Strong  X-rays.     App.  II.     February  21,   1907.     Bar.  75.1  cm.;  temp.  27. 4°  C. 


Cor- 

Cor- 

dp. 

s. 

Cor. 

WP. 

20   C. 
n  X  io-3. 

rected 
io  Xw-3. 

dp. 

s. 

Cor. 

3PJP- 

20   C. 
wXio-3. 

rected 
io  Xw~3. 

(2)  18.6 
19-5 

2.4 
7.0 

cor 

o.  248 
.  260 

3-2 

83 

. 

4 
96 

X-rays  off.    Dust-free  air.    Bar.  75.5; 
temp.  27.2°  C. 

20.4 

10.8 

W  0 

.272 

307 

357 

21.4 

12. 

gy 

.285 

557 

648 

(3)37-6 

13 

bg 

0.500 

1130 

1380 

21.9 

.... 

gy 

.292 

566 

662 

34-9 

13 

g 

-465 

969 

1170 

23.0 

.... 

g 

•  306 

654 

765 

32.8 

g' 

•437 

834 

1007 

24.1 

.... 

g 

.321 

766 

902 

30.1 

13 

gto 

.401 

7i3 

856 

25-9 

g! 

•345 

904 

1071 

gy 

33-7 

13 

w  o 

•449 

650 

784 

27.9 

10 

r 

•372 

367 

437 

33-6 

12 

w  o 

.448 

650 

784 

25-8 

4-7 

cor 

•344 

30.8 

36 

39-9 

small- 

w o 

•532 

640 

782 

24.0 

3-2 

cor 

.320 

8-9 

10 

er 

22.7 

2-5 

cor 

.302 

4-2 

5 

TABLE  33. — Strong  X-rays.     App.  I.     Bar.  76.5  cm.  temp.  22.5°  C.     February  22,1907. 


Cor- 

o  r\ 

Cor- 

dp. 

s. 

Cor. 

dp/p. 

20°  C. 

wXio-3. 

rected 
wXio-8. 

dp. 

S. 

Cor. 

dp/p. 

20   C. 
wXio-3. 

rected 
wXio-8. 

(4)  19-4 

o 

0.254 

0 

o 

X-rays  off.    Dust-free  air.    Bar.  76.7; 

19.7 

4-9 

.258 

28 

29 

temp.  22.  4°  C. 

20.5 

8.8 

c 

.268 

161 

170 

21.4 

10.7 

W  0 

.280 

357 

357 

22.0 

12.8 

yo 

.288 

436 

460 

(5)34-2 

g 

0.447 

1060 

"34 

23-4 

13-5 

gyo 

.306 

584 

617 

31.0 

g 

•  405 

899 

960 

24-5 

gy 

.321 

680 

721 

27.7 

'*-5 

w/bg 

-362 

187 

199 

24.8 

g' 

-324 

766 

812 

25-6 

2-5 

.  .  .  . 

•335 

4-5 

5 

29.7 

.  .  .  . 

g 

.388 

988 

1052 

23.6 

1.8 

•309 

i-5 

1.6 

34-6 

g 

.452 

1066 

1140 

22.2 

1.2 

.... 

.  290 

•4 

•4 

NUCLEATION     CONSTANTS     OF    CORONAS.  7$ 

47.  Conclusion. — The  new  results  lead  to  about  the  same  conclusions 
as  the  older  data  given  above.  The  endeavor  to  obtain  the  negative  and 
positive  steps  of  the  ionization  fails  in  my  apparatus.  Sometimes  there 
are  suspicious  breaks  in  the  nucleation  curve  supporting  such  a  tendency ; 
but  it  is  not  sustained. 

What  I  always  get  is  division  of  the  totality  of  ions  into  two  groups — 
a  numerically  small  group  with  large  nuclei,  and  a  numerically  large 
group  with  relatively  small  nuclei  containing  all  the  ions.  This  occurs 
even  in  such  cases  where  I  catch  the  vapor  nuclei  of  dust-free  air  in 
presence  of  the  ions  (radium  at  Z)  =  4o  cm.),  and  hence  all  ions,  positive 
and  negative,  must  have  been  caught  in  an  earlier  stage  of  the  exhaustion. 

The  slopes  of  the  air  graph  and  the  strong  X-ray  graph  represent  the 
initial  branches  of  a  general  law  of  distribution  of  molecular  aggregates 
such  as  is  given  by  the  theory  of  dissociation.  They  may  therefore  be 
expected  to  be  similar  in  their  slopes,  as  they  actually  are.  The  results 
therefore  bear  on  the  molecular  structure  of  vapors. 

The  question  is  finally  to  be  asked  why  I  catch  the  negative  ions,  etc., 
at  an  apparently  much  lower  supersaturation  than  C.  T.  R.  Wilson.  I 
have  entertained  doubts  whether  the  inertia  of  the  piston  in  his  appara- 
tus is  initially  quite  negligible ;  whether  in  any  apparatus  the  computed 
adiabatic  temperatures  were  actually  reached.  Nobody  has  proved  it, 
and  the  case  should  be  worst  for  small  tubes.  Moreover,  in  every  appa- 
ratus there  must  be  a  limit  at  which  the  smaller  nuclei  of  a  graded  system 
can  no  longer  be  caught  in  the  presence  of  the  larger  nuclei.  There  is  a 
remote  possibility  that,  whereas  in  the  plug-cock  fog  chamber  the  exhaus- 
tion starts  rapidly  but  ends  off  with  retardation,  in  Wilson's  apparatus 
it  may  start  with  relative  slowness  but  finish  with  accelerated  rapidity. 
If  the  lower  limits  of  condensation  were  due  to  emanations  of  metallic 
or  other  material  coming  from  the  vessel,  the  effect  should  vary  with 
the  intensity  of  the  ionization,  which  it  does  not.  If  it  were  due  to  the 
use  of  filtered  air  in  place  of  stagnant  air,  as  in  Wilson's  apparatus,  it 
should  be  equally  evident  with  non-ionized  air,  where  the  limit  of  con- 
densation agrees  with  Wilson's  point  for  negative  ions. 

The  chief  results  of  this  section  will  be  found  in  the  charts,  corre- 
sponding points  of  which  have  been  connected  with  straight  lines  with 
no  attempt  at  smoothing.  In  case  of  the  air  lines,  results  made  at 
long  intervals  of  time  apart  have  been  summarized. 


CHAPTER    IV. 

THE  NUCLEATION  CONSTANTS  OF  CORONAS— CONTINUED. 
ON  A  METHOD  FOR  THE  OBSERVATION   OF  CORONAS. 

48.  Character  of  the  method. — In  the  usual  practical  experiments 
with  the  large  coronas  of  cloudy  condensation  (the  largest  types  having 
angular  diameter  of  nearly  60°),  the  source  of  light  is  placed  in  the 
equatorial  (vertical)  plane  of  the  fog  chamber  and  remote  from  it. 
The  eye  and  goniometer  are  put  as  near  it  as  possible  whenever  sharp 
vision  is  essential.  The  diffracted  rays  in  such  cases  come  from  the 
fog  particles  at  the  ends  of  the  chamber,  as  in  fig.  24,  a,  and  are  liable 


d 


FIG.  24. — (a)  Diffractions  from  fog  particles  at  a,  b,  c,  and  a  single  source  S,  reaching 
the  eye  at  e.  (b)  Diffractions  from  fog  particles  at  a,  b,  c,  and  two  sources  S',  S", 
with  coronas  n  n'  and  n'  n",  in  contract  at  nf,  reaching  the  eye  at  c.  (c)  Diagram 
showing  the  relation  of  S,  s',  s,  R,  r,  6.  (d)  Case  of  two  sources  and  coronas  in  con- 
tact at  n'  drawn  to  scale. 

to  be  seriously  distorted  by  the  refraction  of  the  glass  walls.  Further- 
more, the  limit  will  be  reached  sooner  or  later,  in  which  the  fog  particles, 
to  which  the  diffractions  are  due,  lie  at  or  beyond  the  ends  of  the  fog 
chamber,  after  which  the  features  essential  to  the  measurement  will  no 
longer  appear.  Moreover,  one  eye  only  can  be  used  in  the  measure- 
ments. In  fig.  24,  a,  with  a  source  at  5  and  an  eye  at  e,  the  diffractions 
of  the  fog  particles  a,  b,  c  overlap. 


NUCLEATION    CONSTANTS     OF    CORONAS.  77 

It  occurred  to  me,  therefore,  to  invert  the  phenomenon  by  using  two 
sources,  which  may  be  moved  symmetrically  towards  or  from  the 
equatorial  plane,  as  in  fig.  24,  b,  and  to  observe  the  contact  in  this  plane 
of  the  two  identical  coronas  produced.  In  this  way  the  oblique  refrac- 
tions are  diminished  as  far  as  possible,  coronas  of  all  sizes  are  observable, 
and  both  eyes  are  available  for  observation,  increasing  sharpness  of  vision 
and  lessening  the  eye  strain.  The  contact  method  is  in  itself  more 
sensitive,  seeing  that  the  eyes  may  be  placed  all  but  in  contact  with  the 
fog  chamber.  In  fig.  24,  6,  with  two  sources  at  S'  and  S"  and  the  coronas 
nnf  and  n'n"  in  contact  at  nf  at  the  edge  of  a  given  annulus,  the  diffrac- 
tions of  the  fog  particles  a,  b,  c  overlap. 

49.  Apparatus. — Fig.  24,  d,  shows  a  general  disposition  of  the  appa- 
ratus.    S'  and  S"  are  the  two  circular  sources  of  light  lying  in  the  same 
horizontal,  and  movable  in  opposite  directions  in  equal  amounts,  at  the 
control  of  the  observer  at  the  fog  chamber  F.    S'  and  S"  are  therefore 
always  symmetrical  with  respect  to  the  vertical  plane  SR.    The  diffrac- 
tion of  rays  due  to  the  fog  particles  in  F  produces  coronas  seen  at  nnf  and 
nf  n" ,  and  the  lamps  S'5"  have  been  adjusted  at  a  distance  5,  so  that 
the  selected  annuli  of  the  coronas  are  in  contact  at  n' '.     The  angular 
radii  of  the  coronas,  marked  0  or  shaded  in  the  diagram,  are  nearly 
equal  and  2R  tan  6  =  5,  where  R  is  the  distance  of  the  axis  of  the  fog 
chamber  from  the  track  5. 

On  a  double  track,  at  5,  the  two  carriages  for  the  lamps  S'S"  are 
moved  with  sprocket  and  chain  or  in  a  similar  manner,  and  provided 
with  a  scale  stretched  between  them,  reading  to  centimeters.  This  scale 
is  a  lath  of  wood  about  3  meters  long,  with  one  end  fastened  at  S',  the 
other  free,  while  the  scale  moves  across  an  index  at  S".  A  pole  at  R,  with 
the  end  in  the  observer's  hand,  moves  the  twro  central  sprockets  and  at 
the  same  time  serves  for  the  measurement  of  R,  should  this  vary. 

50.  Errors. — Fig.  24  shows  clearly  that  the  angle  of  diffraction  cor- 
responding to  the  fog  particles  a,  b,  c,  nearer  and  farther  from  the  eye, 
will  not  be  the  same,  and  that  this  effect  will  vanish  as  the  coronas  are 
smaller,  as  the  diameter  or  thickness  of  the  fog  chamber  is  less,  and  as 
the  distance  R  from  the  source  is   greater.     Slightly  different   annuli 
overlap;    but  the  effect  is  much  less  here  than  in  the  case  of  a  single 
source,  where  the  active  fog  particles  lie  oblique  to  the  axis.     (See  fig. 
24,  a,  and  fig.  24,  b,  at  a,  6,  c.)  In  practice  this  effect  is  probably  negligible 
if  the  dimensions  of  apparatus  and  disposition  of  parts  are  properly 
chosen,  particularly  so  since  the  fog  particles  themselves  are  not  usually 
so  nearly  of  a  size  as  to  imply  less  overlapping.    In  fact  the  true  corona, 
if  large  or  even  of  moderate  size,  is  seen  but  for  an  instant  immediately 
after  exhaustion.    It  thereafter  shrinks  rapidly,  as  may  be  gathered  from 


CONDENSATION    OF   VAPOR   AS    INDUCED   BY    NUCLEI    AND   IONS. 


the  incidental  data  shown  in  table  34,  obtained  with  fog  particles  about 
0.0002  cm.  in  diameter,  belonging  to  the  large  yellow-blue  corona. 

TABLE  34. — Contraction  of  coronas  during  subsidence.    Bar.  75.2  cm.;   temp.  27°  C.; 

0.408;    factor  i. 56;    temp,  factor  0.027. 


/. 

5. 

S. 

wXio~3. 

t. 

S. 

s. 

nXio-3. 

I.          sec 

II         sec 

o 

12.  0 

14.4 

920 

0 

12.5 

15-0 

1140 

30 

IO.2 

12.2 

600 

30 

10.8 

13.0 

730 

60 

8.4 

IO.  I 

350 

60 

8.8 

10.6 

400 

90 

7-3 

8.8 

220 

90 

7-4 

8.9 

230 

1000      N 


600  _X_> 


The  coronas  shrink  as  the  fog  particles  increase  in  number  and  de- 
crease in  size  at  an  accelerated  rate.    The  initial  rates  must  be  estimated 

at  a  decrement  of  number 
greater  than  i .  4  per  cent  per 
second,  supposing  that  no 
water  is  added  from  other 
sources  than  the  evaporation 
of  smaller  particles.  In  100 
seconds  about  80  particles 
have  escaped  out  of  each 
100.  The  case  is  much  more 
serious  for  larger  coronas,  so 
that  these  are  characteristic- 
ally fleeting  and  must  be  ob- 
served at  once.  It  may  not  be 
impossible  that  rapidity  of 
evaporation  itself  sets  a  limit 
to  the  largest  coronas  pro- 
ducible. The  nuclei,  however, 
are  not  lost  as  a  rule.  They 
occur  as  water  nuclei  and  are 


400 


ZOO 


0&eC.     ZO         40         BO 

FIG.  25. — Nucleation  n,  computed  from  aperture 
s  of  the  coronas,  gradually  shrinking  during 
the  subsidence  within  100  seconds  after  ex- 
haustion. 


available  for  the  next  coronas,  if  not  removed. 

It  follows,  then,  that  for  these  cases  the  method  of  subsidence  is  not 
applicable,  as  the  corona  changes  totally  before  measurable  subsidence 
is  recorded.  Hence  an  instantaneous  procedure  like  the  goniometer 
method  or  the  present  method  is  alone  available. 

51.  Data. — In  table  35  I  have  inserted  results  obtained  with  phos- 
phorus nuclei,  leaving  out  the  initial  fogs.  It  is  seen  at  once  that  large 
coronal  diameters  are  actually  measurable,  a  result  not  possible  hitherto. 
Reduced  to  the  goniometer  method,  the  present  results  may  be  written 
o.i 2  5=5',  for  small  coronas;  but  for  large  coronas,  if  6  is  the  an- 


NUCLEATION    CONSTANTS    OF    CORONAS. 


79 


TABLE  35. — New  apparatus.  Two  coronas  in  contact.  Bar.  75.6cm.;  temp.  24.7° C.; 
S=2R  tan  6;  #  =  250  cm.;  cock  open  5  seconds;  interval  i  minute.  dp  3=17. 6', 
[£/>2]=i6.8;  phosphorus  nuclei,  ^=0.771;  dpa/p  =  o.233;  w=4.2  g/cm3;  0  =  0.0032; 
5'-6.5. 


Exp. 

No. 

S. 

Cor. 

s. 

o-*n'  = 
0.244*3. 

nx  X  io-3. 

wXio-3. 

£  =  0.16 
Xw1/3 

'  =  O  .  1  2S. 

cm. 

i. 

i 

?2IO 

o' 

19-3 

.... 

3660 

24.6 

2 

185 

0 

16.7 

.... 

2770 

22.4 

3 

165 

TO 

15-4 

.... 

.... 

2080 

20.5 

.... 

4 

H5 

C 

H-3 

.... 

.... 

1560 

18.6 

.... 

5 

130 

stone  bl. 

13-3 

.... 

.... 

1160 

16.8 

.... 

6 

120 

g' 

12.5 

.... 

.... 

862 

15.4 

7 

H3 

gy 

ii.  9 

.... 

.... 

636 

13-8 

8 

104 

gy 

ii  .  i 



467 

12.4 

9 

97 

yo 

10.5 

.... 

34i 

II  .2 

10 

90 

o 

9-9 

.... 

247 

IO.O 

.... 

ii 

78 

C 

8.8 

178 

9.0 

12 

65 

g 

7-4 

98.8 

2880 

125 

8.0 

.... 

13 

60 

gy 

6.9 

80.0 

3430 

85-1 

7.0 

H 

55 

r 

6.4 

63-9 

4130 

56.5 

6.1 

15 

45 

cor 

5-3 

36.4 

3633 

36.6 

5-3 

16 

36 

cor 

4-3 

19.4 

3265 

21.7 

4-5 

.... 

i? 

30 

cor 

3-6 

11.4 

3830 

10.9 

3-6 

.... 

18 

23 

cor 

2.8 

5-4 

4720 

4.2 

2.6 

.... 

19 

18 

cor 

2.2 

2.6 

1750 

•  5 

1-3 

.... 

20 

o 

absent 

0.0 

0.0 



o.o 

.... 

.... 

2. 

i 

?2IO 

0' 

19 

22OI 

20.8 

25.0 

2 

198 

0 

18.6 

.... 

1679 

19.0 

23-8 

3 

185 

c 

17.9 

.... 

1278 

17-3 

22.2 

4 

174 

w' 

18.1 

.... 

973 

15.8 

22.1 

5 

158 

st.  bl. 

16.1 

.... 

740 

14.5 

19.0 

6 

135 

g 

14-3 

.... 

559 

13-1 

16.2 

7 

118 

gy 

12.8 

.... 

420 

12.0 

14.2 

8 

101 

0 

II.  2 

.... 

313 

10.9 

12.  I 

9 

88 

r 

IO.O 

.... 

230 

9.8 

10.6 

10 

75 

r 

8.6 

.... 

167 

8.8 

9.0 

ii 

65 

gy  ° 

7-6 

.... 

118 

7-9 

7.8 

12 

58 

r 

6.8 

84.0 

2269 

81.5 

6-9 

7.0 

13 

5i 

cor 

6.0 

55-6 

2250 

54-4 

6.1 

6.1 

14 

45 

cor 

5-3 

38.5 

2452 

34-6 

5-2 

5-4 

15 

35 

cor 

4-2 

18.1 

1927 

20.7 

4-4 

4-2 

16 

28 

cor 

3-4 

9.6 

2106 

IO.O 

3-5 

3-4 

17 

21 

cor 

2-5 

3-8 

2462 

3-4 

2.4 

2-5 

18 

?i5 

very 

1.8 

1.4 

2680 

i.i 

1.6 

1.8 

small 

3- 

i 

?2IO 

o' 

19.0 



2010 

20.1 

25.0 

2 

195 

o 

18.4 

.... 

.... 

1534 

18.4 

23-4 

3 

175 

w' 

17.2 

.... 

Il67 

16.8 

21  .O 

4 

158 

v 

16.1 

.... 

.... 

885 

15-4 

I9.O 

5 

145 

g 

15.0 

.... 

.... 

670 

14.0 

17.4 

6 

133 

gy 

14.1 

.... 

505 

12.7 

16.0 

7 

I  2O 

y  o 

13.0 

.... 

379 

ii.  5 

14.4 

8 

106 

0 

ii.  7 

282 

10.6 

12.7 

9 

88 

c 

IO.O 

.... 

.... 

209 

9-4 

10.6 

10 

74 

g 

8-5 

.... 

151 

8-5 

8-9 

ii 

60 

g 

7.0 

91.0 

1708 

107 

7-6 

7.2 

12 

57 

r 

6.6 

76.6 

2133 

72.2 

6.7 

6.8 

J3 

49 

cor 

5-7 

50.0 

2105 

47.8 

5-8 

5-9 

14 

4° 

cor 

4-7 

27.0 

1813 

29.9 

5-0 

4.8 

15 

33 

cor 

4.0 

15-6 

1898 

16.5 

4.1 

4.0 

16 

27 

cor 

3-2 

8.0 

2104 

7-5 

3-i 

3-2 

17 

21 

cor 

2.5 

3-8 

3881 

2.1 

2.0 

2-5 

18 

.... 

just 

.... 

.... 

.6 

1.0 

.... 

visible 

8o 


CONDENSATION    OF    VAPOR    AS    INDUCED    BY    NUCLEI    AND    IONS. 


gular  diameter,  S  =  2R  tan  0,  s  =  2r  sin  6,  or  5  =  8.3  s/\/i — s2/4r2, 
5=0.12  5/Vi +52/4^2,  ^  =  250  cm.,  ^  =  30  cm.  Fig.  24,  c,  shows  the 
relation  of  these  quantities.  Since  the  elementary  diffraction  equation 
may  be  put 

sin  0  =  i  .22  XI d 
for  the  first  minimum 


5  =(2.  44  R  */d)/Vi—(i.22  XI  d)* 

and  5  would  therefore  appear  to  be  less  immediately  adapted  for  the 
equation  than  s.  It  does  not  follow,  however,  that  this  5  and  the  one 
observed  at  the  goniometer  work  are  the  same.  In  fact  they  are  not, 
the  latter  being  larger  for  reasons  involved  in  the  more  recondite  theory 
of  the  experiment,  or  else  due  to  irregular  refractions  at  the  remote 
ends  of  the  chamber.  In  practice  5  will  usually  be  preferred  to  5. 

In  table  35,  ^  =  0.771  =  (p—[dp2]—n)/(p—K)  ;  0^3/^-0.233;  ioew  = 
3.80  at  20°;  therefore  at  25°,  10  per  cent  higher  or  io6m  =  4.i8  grams 
per  cubic  centimeter.  Hence  n'  =  6ms3/xa3  =  o.  244  s3/ios.  The  value  of 

TABLE  36.  —  New  apparatus.    Two  coronas  in  contact.    Bar.  7  6.  4  cm.;   temp.  =  2  7°  C; 


S=2R  tan  0;    ^  =  250  cm.;    cock  open  5  seconds;    interval  i  minute.     d 
2]  =  9.2.     Phosphorus  nuclei.     dp3/p  =  o.i2O',    ^  =  0.875;    io6w=2.33; 


6.5. 


Exp. 

No. 

s. 

Cor. 

Sr  =  I  2S. 

IO3«'  = 

0.136^. 

MjXlO-3. 

wXio~3. 

s  =  o.i94w1/3. 

4- 

i 

>  2IO 

o-fog 

25.0 

1888 

24.0 

2 

2OI 

o 

24.1 

.... 

1635 

23-0 

3 

194 

o 

23-3 

.... 

1414 

21.8 

4 

1  88 

o 

21.4 

1222 

20.9 

5 

173 

r 

20.8 

.... 

1053 

19.9 

6 

1  60 

c 

19.2 

907 

18.9 

7 

146 

c 

17.5 

779 

17.9 

8 

131 

v'c 

15-7 

667 

17.0 

9 

116 

v' 

13-9 

567 

16.2 

10 

105 

v'g 

12.6 

479 

15.2 

ii 

98 

v'g 

ii.  8 

402 

14.4 

12 

98 

v/  g 

ii.  8 

335 

13-5 

13 

98 

g 

n.  8 

280 

12.8 

H 

95 

gy 

11.4 

233 

12.0 

15 

94 

yo 

ii.  3 

194 

ii.  3 

16 

94 

yo 

ii.  3 

161 

10.6 

17 

88 

w  r 

10.6 

133 

99 

18 

88 

we 

10.6 

no 

9-4 

19 

80 

wp 

9-6 

90.3 

8.8 

20 

72 

cor 

8.6 

73-2 

8.2 

21 

67 

g' 

8.0 

.... 

58.5 

7-6 

22 

61 

gy 

7-3 

.... 

46.1 

7.0 

23 

54 

w  r 

6-5 

37-4 

1995 

35-4 

6.4 

24 

48 

r 

5-8 

26.5 

1913 

26.1 

5-8 

25 

42 

cor 

5-0 

17.0 

1748 

18.4 

5-2 

26 

37 

cor 

4-4 

12.0 

1895 

12.  O 

4-5 

27 

28 

cor 

3-4 

5-2 

7.0 

3-7 

28 

22 

cor 

2.6 

2-5 

2-5 

2.7 

29 

17 

cor 

2.0 

I  .  2 

0.9 

i-9 

30 

0 

.... 

0.0 

O 

.... 

0-3 

i-4 

i 

NUCLEATION     CONSTANTS     OF    CORONAS.  8l 

the  subsidence  constant  S'  =  6 .  5  is  taken  as  the  mea  value  of  the  above 
data.  To  compute  5  =  an1'3/  (6m/  ?r)1/3,  the  reduced  values  are  5=0.  i6n1/3. 
In  table  36  the  exhaustion  ^  =  0.771  is  smaller  and  the  temperature 
27°.  The  constants  have  the  corresponding  values  shown  at  the  head  of 
the  table. 

52.  Remarks  concerning  the  tables,  and  conclusion. — The  first  series  in 
table  34  contains  data  both  for  5,  0.12  5=5'  and  s,  and  leads  to  a  cu- 
rious consequence.  The  computed  chords  of  the  coronas,  s  =  a(nn/6m)lf3, 
is  not  proportional  to  s  =  2r  sin  6  but  to  S  =  2R  tan  6,  where  26  is  the 
angular  diameter  of  the  coronas.  This  implies  a  diffraction  equation  read- 
ing tan  6  =  1.2  2  X/d. 

These  results  are  shown  in  fig.  26,  where  s  cc  n1/3  is  laid  off  as  the 
abscissas  and  0.12  5  oc  tan  6  and  o.  i25/Vi  +  S2/4-R2  oc  sin  6,  as  or- 
dinates.  If  we  confine  our  attention  to  values  within  5  =  14,  where  the 
readings  are  more  certain,  and  where  there  is  less  accentuated  over- 
lapping of  coronas,  the  graph  0.12  S  oscillates  between  two  straight 
lines  as  the  coronas  change  from  the  red  to  the  green  types.  The  slopes 
of  these  lines  are  respectively  as  i  .08  =  73 . 2  X^ja  and  0.99  =  73 . 2  >l2/a, 
whence  ^1=  0.000047  an(^  ^2  =  0-000°43  cm-  These  should  be  blue  and 
violet  minima. 

Fig.  26  shows,  moreover,  that  compared  with  the  graph  for  0.12 
5  =  6o  tan  6,  the  curve  for  sin  6  is  in  series  i  quite  out  of  the  question, 
as  already  specified.  Hence  in  the  remaining  series  of  observations  in 
tables  35  and  36,  0.12  5  was  used  in  place  of  s.  The  results  for  the 
series  2,  3,  4,  are  also  given  in  fig.  26,  in  the  same  way.  Curiously 
enough,  series  2  and  3,  which  should  be  identical  with  i,  fail  to  coincide 
with  it  in  the  region  of  higher  coronas.  In  these  series  the  graph  s  oc  sin  0 
would  more  nearly  express  the  results,  though  the  agreement  is  far  from 
satisfactory.  Series  4  again  corroborates  series  i,  needing  the  sf  oc  tan  0 
graph  for  its  nearest  expression;  but  in  this  series  there  is  a  curious 
horizontal  part  corresponding  to  observed  coronas  of  the  fixed  type 
in  the  middle  region  of  green  coronas  (5  =  10  to  12),  showing  that  the 
periodicity  has  been  exaggerated. 

It  is  exceedingly  difficult  to  account  for  this  difference  of  behavior. 
One  may  suppose  that  the  phosphorus  nuclei,  which  are  here  solutional 
water  nuclei,  are  not  quite  of  the  same  size.  This  may  happen  if  the 
air  is  unequally  saturated,  for  instance.  In  such  a  case  the  coronas 
would  be  largest  when  the  air  is  most  nearly  homogeneous  and  the 
nuclei  gradient  within  narrow  limits  (series  2  and  3),  whereas  in  less 
favorable  cases  (series  i  and  4)  smaller  coronas  would  appear.  As  the 
abscissas,  s  =  a  (n^r/am)1/3,  where  n2=^2-Jn  and  the  ordinates  s  (ob- 
served) are  independent  of  each  other,  the  equality  of  s'  and  5  will  in  a 
measure  check  the  work  apart  from  the  constant  a  which  determines  n0. 
This  is  actually  the  case  for  the  lower  series  of  coronas  below  5  =  10. 


82  CONDENSATION    OF   VAPOR   AS    INDUCED   BY   NUCLEI    AND   IONS. 

\ 


NUCLEATION    CONSTANTS    OF     CORONAS. 


On  the  other  hand,  it  is  the  observational  value  of  the  aperture  of  the 
given  coronas  which  varies.  Thus  in  fig.  26  the  green  coronas  vary  from 
5  =  12  to  5  =  17  in  the  different  series.  Very  probably  mixed  coronas 
are  being  observed.  To  this  must  be  added  the  subjective  error  or 
personal  equation  which  enters  into  the  determination  of  contacts. 
Finally,  the  tendency  of  a  corona  to  shrink  at  once  after  the  formation 
of  droplets  makes  it  difficult  to  catch  the  time  at  which  coronas  should 
be  observed  soon  enough.  Under  other  circumstances  there  is  even 
liable  to  be  an  oscillation  of  the  coronal  aperture  in  the  lapse  of  time. 
All  these  difficulties  are  accentuated  as  the  coronas  become  larger,  for 
here  not  only  are  the  droplets  more  volatile,  but  the  coronas  overlap, 
and  there  is  an  unlooked-for  tendency  for  them  to  flatten  at  the  point 
of  contact.  Th$  dark  rings  are  liable  to  invade  the  bright. 

The  green  coronas  in  table  34,  series  i  and  2,  and  table  35,  series  3, 
show  the  following  average  values: 


Computed. 

Observed. 

Computed. 

Observed. 

vSeries 

,, 

S2. 

ss. 

S2. 

io^3. 

,oV, 

,0^ 

i 

8 

16 

8 

14 

400 

200 

400 

230 

2 

8 

H 

8 

15 

400 

230 

400 

2IO 

3 

8 

13 

8 

13 

400 

250 

4OO 

260 

Mean  values  are  thus 

53  =  8 .  o         i  oe<i3  =  400  $2=14.3         J  °6^2 

agreeing  pretty  well  with  the  above  data  (Chapter  III,  section  33),  where 

$3=   8.1          10^3  =  398  52==I4-0         io6J2  =  228 

I  may  summarize,  in  conclusion,  that  the  present  section  has  developed 
the  method  of  observation  by  which  data  are  obtained  from  the  distance 
apart  of  two  sources  of  light  when  certain  fiducial  rings  of  the  coronas 
are  put  in  contact.  This  method  is  superior  to  the  above  method  with  a 
single  source  of  light,  although  its  full  value  has  not  been  evidenced, 
because  of  the  extreme  sensitiveness  of  the  coronas  to  differences  in  the 
distribution  of  the  density  of  the  nucleation.  There  is  a  second  difficulty 
inherent  in  the  phenomenon  itself,  viz,  the  shrinkage  or  oscillation  in 
the  size  of  coronas  following  the  instant  of  their  formation.  It  is  prob- 
able that  the  number  of  fog  particles  actually  decreases  by  evapora- 
tion, though  the  phenomenon  is  complicated  by  the  coincident  variation 
of  temperature.  After  relatively  long  waiting,  a  somewhat  similar 
shrinkage  takes  place  throughout  the  period  of  subsidence,  and  in  case 
of  large  coronas  the  apparent  nucleation  may  thus  be  reduced  to  one- 
fifth  of  its  original  value. 


84  CONDENSATION    OF    VAPOR   AS    INDUCED   BY    NUCLEI    AND    IONS. 

DISTRIBUTIONS  OF  VAPOR  NUCLEI  AND  OF  IONS  IN  DUST-FREE 

WET  AIR. 

53.  Behavior  of  different  samples  of  radium.     New  fog  chamber.— 

It  was  my  hope  to  be  able  to  obviate  the  need  of  using  the  trouble- 
some and  inconstant  X-ray  bulb  by  replacing  it  by  a  strong  sample  of 
radium.  It  also  seemed  possible  that  the  fog  chamber  might  be  stand- 
ardized in  this  way;  but  the  attempts  proved  quite  abortive,  as  indeed 
might  have  been  expected.  The  coronas  were  but  slightly  increased  on 
intensifying  the  original  activity  of  radium  I,  100  mg.  10,000  X  ,  equiva- 
lent to  say  io6,  by  adding  radium  II,  10  mg.  2oo,oooX,  equivalent  to 
2X10";  radium  III,  100  mg.  io,oooX,  equivalent  to  iXio6;  radium 
IV,  100  mg.  1 0,000 X  ,  equivalent  to  i  X  io6;  radium  V,  100  mg.  20,000 X  , 
equivalent  to  2Xio6;  on  the  whole,  therefore,  about  seven  times. 
Obviously  the  radium  must  be  kept  sealed  in  tubes  of  aluminum  or  of 
very  thin  glass,  as  otherwise  the  fog  chamber  would  become  infected, 
which  would  be  fatal  to  experiments  of  the  present  character. 

The  reason  of  the  relative  inefficiency  of  the  radium  is  given  by  the 
equation  — dn/dt  =  a — bri*,  where  a  is  the  number  of  ions  generated  per 
second  and  bn2  the  number  which  decay  per  second.  Hence  for  the 
case  of  equilibrium  a/b  =  n2,  where  a  varies  as  the  activity  of  the  radium. 

If  the  five  samples  in  question  be  taken  together,  therefore,  the 
equilibrium  nucleation  n  would  be,  for  any  fixed  distance  of  the  radium 
from  the  fog  chamber, 


Now,  n  varies  as  S3  (if  5  be  the  angular  diameter  of  the  coronas)  in  a 
general  way,  and  therefore  the  resultant 

aocS6 

Consequently  enormous  increases  of  the  nucleation  bring  about  but 
slight  changes  of  the  angular  diameter  of  the  coronas.  This  estimate 
is  not  quite  correct  if  the  values  of  b  vary,  as  seems  to  be  the  case,  with 
the  nucleation;  but  for  the  larger  nucleations  here  in  question  such 
an  effect  is  not  observable.  If  it  can  be  controlled  a  new  method  of 
standardizing  the  fog  chamber  for  moderate  coronas  would  be  suggested. 

54.  Data — Results  of  this  character  are  given  in  table  3  7 ,  wrhere  5  is 
the  double  tangent  of  the  corona  on  a  radius  of  250  cm.,  n  the  nucleation 
corrected  for  the  exhaustion  v1/v  =  1.287.  ^n  addition  to  the  effect 
of  aggregating  the  radium  tubes,  their  position  on  the  outside  of  the 
fog  chamber  is  indicated  as  follows :  a  denotes  that  the  tubes  are  placed 
on  the  outside  of  the  walls  of  the  horizontal  glass  cylinder,  above  its 
middle  or  equatorial  parts;  b  that  they  are  similarly  placed  near  the 
brass  cap  at  the  exhaust  end;  c  that  they  are  placed  near  the  remote 


NUCLEATION    CONSTANTS    OF    CORONAS.  85 

TABLE  37. — Radium  I,  100  mg.  10,000 X,  and  radium  II,  10  mg.  200,000 X  compared. 
Bar.  76. 7  cm.;  temp.  20°  C.;   dpa=22.g  cm.;   3p3/p  =  o.2gg;  1^/1;=  i  .287. 


5.       c 

>.I2S  =  .f'. 

nXio-*. 

io-V. 

2wa. 

44 

(l)  II 

45 

5-3 

39 

1,520 

42 

I  .... 

46 
45 

5-4 

42 

1,810 



I  and  II  at  a  

50 

52 

6.1 

61 

3,720 

3,330 

(2)  The  same,  on  different  parts  of  chamber.   Bar.  76.3;  temp.  18°  C;  ^3/^  =  0.299. 

II  at  c  

61 
62 

7-3 

104 

10,820 

I  at  c  

60 
60 

7.2 

TOI 

10,200 

I  and  II  ate  

65 
67 

7-9 

129 

16,640 

21,000 

II  at  b 

44 
44 

5-3 

39 

1,521 



I  at  6 

41 

38 

4-7 

29 

841 

I  and  II  at  b  

47 
49 

5-7 

50 

2,500 

2,360 

I  and  II  at  b  

46 

5-5 

44 

i,936 

.... 

at  o  

57 

6.7 

80 

6,400 

1  55 

at  c  

(65 
167 

7-9 

129 

16,640 

(3)  II  kept  in  old  place  a  ;  I  placed  on  chamber  at  c  nearer  glass  end  ;  observation  at  c. 

Bar.  76.3  cm.;    temp,  19°  C;    ^3=22.9;    dpz/p=  0.300;  ^  =  1.288. 

V  ate  

66 
66 

7-9 
7-9 

129 
129 

16,600 

.... 

IV  at  c  

62 
59 

7-4 
7-i 

92 
89 

8,300 



Ill  at  c  

59 
59 

7-i 
7-i 

89 
89 

7,900 

Ill  and  IV  ate     

66 
66 

7-9 
7-9 

129 
129 

16,600 

16,200 

Ill,  IV,  and  V  at  c  

7i 
7i 

8.5 

8-5 

162 
162 

26,400 

32,800 

glass  end.  Observations  were  made  with  both  eyes  below  c,  as  this  posi- 
tion showed  the  largest  coronas.  The  marked  reductions  of  size  for  the 
other  positions  of  the  eyes  are  probably  distance  effects,  though  there  are 
necessarily  a  variety  of  complications.  Table  37  shows,  however,  the 
extreme  need  of  placing  all  the  radium  as  nearly  as  possible  on  the  same 
spot,  the  importance  of  which  was  not  at  first  adequately  appreciated 
(compare  series  2).  Radium  placed  at  c  produces  over  eight  times  as 


86          CONDENSATION   OF  VAPOR  AS   INDUCED   BY   NUCLEI   AND   IONS. 

TABLE  37 — Continued. 


S. 

0.125=.?'. 

nX  io-3. 

io-°w2. 

Sw2. 

(4)  Further  comparisons,  all  at  c.   Bar.  76.2;    temp.  20°  C;    dpa/p  =  0.300. 

II                         

1 
i 

66 
68 
69 
7i 
67 
7i 
60 

65 
62 
61 
82 
85 
'72 
175 
73 
[69 
72 

8.0 
8.4 
8.3 

}    r.a 

7-4 

IO.O 

8.8 

8.5 
8.6 

135 
157 
152 

in 

107 
266 

175 
162 
1  66 

18,200 
24,600 
23,100 

12,300 
11,400 
70,800 
30,600 

26,200 
27,600 

89,600 
71,400 

46,800 
23,700 

I  

V  

Ill 

IV 

I  +  II  +  III  +  IV  +  V       

I  +  III  +  IV  +  V  

III  +  IV  +  V     

III  +  IV  

many  nuclei  than  when  placed  at  b  and  over  twice  as  many  than  when 
placed  at  a,  and  the  rate  of  production  of  ions  would  be  as  the  square  of 
these  numbers.  The  effect  is  enhanced  by  the  fact  that  the  lateral  rays 
have  to  pass  obliquely  through  the  glass ;  but  this  appears  to  be  a  minor 
disturbance.  In  all  the  experiments  an  aluminum  gutter  was  cemented 
to  the  top  of  the  fog  chamber  and  the  sample  tubes  of  radium  placed 
between  given  marks  within  it. 


300 


too 


WO        ZOO        300        400 


FIG.  27. — Aggregated  effect  of  beta  and  gamma  rays  of  different  samples  of  radium, 
I,  II,  III,  IV,  and  V,  observed  and  computed  in  terms  of  nucleation  n  produced. 

Table  37  contains  the  values  of  ^n2  for  the  four  series  of  experiments 
given,  and  in  fig.  27  these  data  are  additionally  shown  by  mapping  out 
the  observed  n  as  abscissas  and  the  computed  n  =  \/^n2  as  ordinates. 
There  is  considerable  divergence  from  the  straight  line  which  ought  to 


NUCLEATION    CONSTANTS    OF    CORONAS. 


appear,  reasons  for  which  are  outstanding.  As  a  rule  smaller  values  of 
n  are  observed  than  should  occur,  particularly  for  the  larger  coronas. 
As  a  means  of  standardizing  the  fog  chamber,  therefore,  this  method  is 
again  inapplicable ;  moreover,  strictures  are  cast  on  the  present  theory 
by  Chapter  VI,  where  — dn/dt  =  a  —  bn2  is  called  in  question. 

55.  Distributions  of  vapor  nuclei  and  of  ions. — In  tables  38  and 
39  I  have  collected  data  for  the  number  of  nuclei  and  of  ions  found  in 
apparatus  II,  under  different  conditions.  Not  only  is  a  new  fog  chamber 
used  here,  but  the  method  employed  is  the  one  described  in  the  present 
chapter.  Contact  is  therefore  made  between  the  fiducial  annuli  of  two 
coronas,  and  the  distance  apart  of  the  sources  of  light  or  the  double 
tangent  5,  on  a  radius  of  250  cm.,  at  which  contact  occurs,  is  measured. 
Special  work  was  also  done  to  determine  the  fog  limits;  and  in  case  of 
the  vapor  nuclei  of  dust-free  air,  the  initial  region  of  ions  is  explored  in 
detail  (table  39).  The  table  contains  the  adiabatic  expansion  v1/v  and 
the  relative  adiabatic  drop  dp3/p. 

38. — Certain  distributions  in  apparatus  II.     Bar.  76  cm.;  temp.  18°  C. 


9P» 

5. 

0.125  =  .?'. 

'wXio-3. 

vi/v' 

Spz/p. 

(i)  Radium  I  +  II  

22.8 

72 

8.6 

167 

.288 

0.300 

26.6 

70 

8.4 

176 

•357 

•  350 

26.6 

7i 

8.5 

182 

•  357 

.350 

24.7 

67 

8.0 

144 

.322 

.325 

23.0 

72 

8.6 

1  66 

.  292 

.303 

21  .  I 

65 

7.8 

119 

.  260 

.278 

IQ.  2 

10 

1.2 

0.4 

.230 

.253 

19.2 

10 

I  .  2 

0.4 

.230 

.253 

Fog  limit.    Radium  I  +  II  and  X-rays.    Bar.  76.1  cm.;   temp.  2i°C. 

(2)  Radium  I  +  II  

18.5 

o.o 

O.O 

0.0 

i.  218 

0.243 

19-5 

0.0 

0.0 

0.0 

1-233 

.256 

20.4 

(?) 

(?) 

(?) 

1.247 

.268 

20.4 

17 

2.O 

2-5 

1.247 

.268 

Bar.  76.0  cm.;  temp.  2i°C. 

(3)  Radium  I  +  II  

18.3 

o 

0 

o.o 

.216 

o.  241 

18.8 

o 

O 

o.o 

.222 

.247 

19-3 

9 

II 

0.3 

.231 

•254 

19-3 

9 

II 

0.3 

.231 

•254 

(d.~)  X-ravs  •    D  =  i  s  .  . 

19-5 
18.9 

22 
10 

26 
12 

4.6 

o-3 

•234 
.225 

•257 
.249 

D  —  10 

IQ    I 

13 

16 

0.9 

.227 

.251 

I8.5 

O 

0 

o.o 

.219 

•243 

1  Ions  under  radiation  not  lost  by  exhaustion. 


88          CONDENSATION   OF   VAPOR   AS   INDUCED   BY   NUCLEI   AND   IONS. 
TABLE  39. — Distributions  of  vapor  nuclei  in  dust-free  air.     Bar.   75.9  cm.;    temp.    2i.5°C 


8p» 

S. 

S*. 

n. 

*Pl/P. 

vjv. 

dp*. 

5. 

s'. 

n. 

*PJP- 

V  V. 

(I) 

i9-3 
20.3 

20.8 
21.2 
21.7 
22.0 
22.3 
22.8 
23-3 
23-6 
24.4 
25-3 
26.4 
27.1 
26.9 
27.6 
28.1 
28.9 
29.1 
29-5 
30.5 
31.0 
32.0 
32.0 

33-5 
35-4 
38.0 

o 
13 
14 
H 
15 
H 
15 
15 
17 
19 
19 
26 
30 
52 
45 
769 
72 
81 
€97 
r  102 
Y  129 
g'  128 
g'  140 
g  136 
g  H7 
v'?  140 
v7?  140 

o.o 
.6 
•  7 

•  7 
.8 

'.8 
.8 

2.O 
2-3 
2-3 

3-i 
3-6 

6.2 

5-4 
8-3 
8.6 

9-7 
ii.  6 

12.2 
15-5 
15-4 

16.8 

16.3 
17.6 

?!7-0 

?i8.o 

o.o 
0.9 

1.2 
I  .  2 

1-4 
I  .2 

i-5 

1.5 

2.O 

3-3 
3-4 
8.6 
14.7 
74.0 
47.0 
176 
194 
289 
480 
560 

I2IO 

1225 
1533 
1431 
1780 
1670 
2090 

0.254 
.267 

.275 
.279 
.286 
.290 
.294 
.300 
•307 
•311 
•322 

•333 
•348 
•357 
•355 
•364 
•370 
.381 
•383 
•389 
.402 
.410 
.422 
.422 
•442 
.466 
.500 

.231 
.246 
.256 
.262 
.270 

•  275 
.280 
.288 

•  297 
.302 

.318 
•333 
•354 
.368 

•365 
•378 
•  388 
•405 
.408 
.418 
.440 

•454 
.476 
.476 

•513 
.561 
•635 

Radium  removed  from  the  room.  Bar. 
75.1;  temp.  22°  C.  Vapor  nuclei. 

(2) 

19.4 
20.  i 
20.3 

0 
10 
10 

0 
I  .2 
1.2 

o.o 
0.4 
0.4 

0.258 
.268 
.270 

i  •  235 
1.248 
1.250 

X-rays.  D=io;  bar.  75.1  cm.;  temp.  22°  C. 

(3) 

18.5 
19-5 

20.8 

20.9 

21.7 
21.9 
22.4 

23.0 

23-4 
25.0 
30.0 

35.1 

?  10 

26 

r  89 
ybiis 
g'o  135 
g  130 
g  131 
g'i36 
131 
132 

134 
136 

1.2 

3-i 

10.7 
13-8 

16.2 

15.6 

15.7 

16.3 
15.7 

15.8 

16.1 
16.3 

o.4 
7-i 
303 
654 
1074 

959 
1017 
1130 
1058 
1107 

I3i7 
1486 

0.246 
.260 

.277 
.278 
.289 
.292 
.298 
•  306 
.312 

•333 
.400 
.467 

.222 
•238 
•259 
.260 

•274 
.278 
•285 
.  296 
•304 

•333 
•437 
•563 

56.  Remarks  on  the  table. — These  results  are  constructed  in  figs.  28 
and  29  in  different  scales,  the  nucleation  of  fig.  29  being  on  a  scale  100 
times  greater,  so  that  it  may  be  in  keeping  with  the  very  low  nuclea- 
tions.  As  a  whole  the  figures  are  very  closely  like  the  above,  though  a 
different  apparatus  was  used.  The  line  for  dust-free  air  and  vapor  nuclei 
here  showed  a  tendency  to  transcend  large  green  coronas,  distinctly 
entering  the  violet  of  the  first  series;  but  as  the  coronas  are  filmy  the 
measurement  is  correspondingly  difficult.  Over  2,000,000  vapor  nuclei 
are  registered  by  the  present  method  in  the  extreme  case. 

In  general,  however,  apparatus  II  shows  fewer  nuclei  than  apparatus 
I  under  like  conditions  of  exhaustion.  Thus  at  ^3/^  =  0.375,  n  =  250,000 
for  I  and  n  =  500,000  for  II;  at  higher  exhaustions,  dps/p  =  o.^gt  n  = 
800,000  to  900,000  for  I,  n  =  600,000  for  II;  at  dps/p  =  o.4o,  n=  900,000 
to  1,000,000  for  I  and  n=  1,200,000  for  II;  but  here  apparatus  I  is 
already  losing  efficiency. 

Fig.  28  also  shows  the  small  nucleations  due  to  radium  I +  11  and 
radium  I  to  V,  as  compared  with  the  enormous  effect  of  X-rays  in 
proper  positions.  In  the  case  of  the  intense  X-rays,  the  striking  rapid 
upward  sweep  of  the  curve  is  noticeable  in  case  of  apparatus  I  as 
compared  with  apparatus  II.  The  asymptote  is  reached  much  more 


NUCLEATION    CONSTANTS    OF    CORONAS. 


89 


CONDENSATION  OF  VAPOR  AS  INDUCED  BY  NUCLEI  AND  IONS. 


suddenly  in  case  of  the  new  results,  and  it  is  perhaps  higher  than  in  the 
old.  No  progress  above  the  green  corona  could  be  obtained,  but  on  the 
other  hand  there  was  no  decrement  of  nucleation  at  very  high  exhaus- 
tions, such  as  is  often  obtained. 

57.  Condensation  limits  and  fog  limits.  Conclusion. — The  conden- 
sation limits,  or  the  exhaustions  at  which  condensation  begins,  are  best 
gathered  from  fig.  29,  which  also  shows  the  nearly  constant  low  nuclea- 
tion (due,  as  C.  T.  R.  Wilson  has  proved,  to  ions),  which  precedes  the 
region  of  vapor  nuclei  in  the  case  of  dust-free  wet  air. 


Series. 

Condensation  limit. 

-vj-v. 

9PJP- 

Radium  I  +  11 

II 
II 
IV 
V 
V 
I 
II 
III 

i  .  240 
(higher) 
.  226 
.225 
.223 
.238 
.241 

.222 

o.  262 

.250 
.249 
.247 
.261 
.263 
.246 

X-rays,  D=io  cm  

Radium  I  +  11 

X-rays  Z?  =  35  cm 

D=  io  cm 

Vapor  nuclei 

Do  

X-rays,  D  =  10  cm  

D  is  the  distance  from  which  the  X-ray  tube  acts. 

It  appears  certain  from  these  results  that  the  condensation  limit 
decreases  slowly  as  the  intensity  of  radiation  increases;  also  that  it  is 
lower  for  ionized  air,  even  under  weak  radiation,  than  for  dust-free 
normal  air.  Coronas  may  be  obtained  in  succession,  in  these  instances, 
after  they  have  completely  vanished  in  the  preceding  case  of  weaker 
radiation.  Rain  is  naturally  accompanied  by  a  definite  corona.  If  we 
reckon  the  intensity  of  the  radiation  as  the  square  of  the  maximum 
radiation  producible,  or  the  height  of  the  asymptote,  the  following  data 
may  be  adduced  from  figs.  28  and  29: 


wXio-3. 

n\ 

Ratio. 

apJP- 

vjv. 

*(V"). 

Wet  air  (dust-free)  
Radium  I  +  11   

i-5 

100  to  150 

2 
I  tO  2XlO4 

i 

I04 

0.26 

25 

1.240 
I    225 

0.0 
.OI5 

X-rays  D=o        .... 

IOOO 

IO8 

IO8 

24.5 

I  .  22O 

.020 

Thus,  while  the  intensity  of  radiation  changes  from  the  natural  radia- 
tion in  dust-free  air,  i,  to  io4  for  beta-gamma  radiations,  and  from  i  to 
io6  for  X-rays,  the  volume  expansion  at  which  condensation  takes  place 
shifts  over  decrements  of  0.015  and  0.020  or  15/1240  and  20/1240, 
i.  e.,  1.2  per  cent  and  i .  6  per  cent. 


NUCLEATION    CONSTANTS    OF    CORONAS. 


In  conclusion,  it  may  be  interesting  to  adduce  mean  values  for  the 
condensation  limits  as  obtained  in  Chapter  III,  with  the  former  appara- 
tus I.  They  are  shown  in  the  table  below,  and  they  agree  well  with 
the  present  set,  remembering  that  the  values  would  be  slightly  below 
these  data  if  taken  from  the  chart. 


dp3/p. 

Vj/Vj. 

Air  alone  .  .  . 

O    26s 

I    24.  "* 

Air  actuated 

by  radium  

.246 

I  .  22"? 

Air  actuated 

by  X-rays  

.  24.^ 

I  .  2  2O 

The  results  of  the  chapter  may  be  summarized  as  follows.  The 
endeavor  to  standardize  the  fog  chamber  by  a  number  of  distinct  but 
similar  samples  of  radium,  used  in  succession,  runs  counter  to  a  great 
difficulty,  inasmuch  as  the  effect  produced  at  the  line  of  vision  depends 
upon  the  position  of  the  radium  tubes  on  the  outside  of  the  fog  chamber. 
Moreover,  the  aperture  of  the  coronas  varies  only  with  the  sixth  root  of 
the  rate  of  production  and  is  therefore  not  a  sensitive  criterion. 

The  results  for  vapor  nuclei  and  ions  are  best  seen  from  the  chart. 
The  deductions  are  similar  to  those  already  given  at  the  end  of  Chapter 
III.  The  positions  of  the  condensation  and  the  fog  limits  have  just 
been  stated.  These  terminal  points,  as  well  as  the  graph  as  a  whole,  are 
reached  at  lower  exhaustions  than  was  the  case  in  Wilson's  experiments. 


CHAPTER   V. 

RESIDUAL  WATER  NUCLEI. 
PROMISCUOUS  EXPERIMENTS. 

58.  Historical. — A  nucleus  obtained  from  a  partial  evaporation  of  fog 
particles  will  be  called  a  residual  water  nucleus  or,  briefly,  a  water  nucleus. 

C.  T.  R.  Wilson,*  in  his  experiments  with  ultra-violet  light,  found 
that  nuclei  were  spontaneously  producible  on  long  exposure  of  dust-free 
air  saturated  with  water  vapor  to  the  radiation.  He  explained  this  as 
being  due  to  the  probable  production  and  solution  of  hydrogen  peroxide, 
wherefore  the  vapor  pressure  at  the  surface  of  the  minute  solvent  water 
droplets  would  be  diminished.  Such  droplets  would  therefore  grow  in 
the  saturated  environment.  Wilson  also  encountered  water  nuclei  pro- 
duced by  evaporation,  but  he  expressed  no  opinion  of  their  nature,  merely 
treating  them  as  an  impurity  to  be  removed  to  make  the  air  dust-free. 

J.  J.  Thomson, f  in  his  famous  experiments,  encountered  similar  dif- 
ficulties with  water  nuclei.  He  states  that 

When  ....  the  number  of  ions  is  large,  experience  shows  that  they  are  not  all 

brought   down   by   the  first  cloud   formed  by  sudden  expansion after  the 

first  cloud  has  subsided,  [and] another  expansion  be  made,  a  second  cloud 

is  formed 

On  page  531,  moreover, 

The  first  expansion  ....  though  it  does  not  bring  all  the  ions  down,  seems  to 
increase  the  size  of  those  left  and  makes  them  more  permanent,  ....  these  modified 
ions  are  able  to  cause  a  cloud  to  settle  with  an  expansion  of  less  than  i .  25  .  .  .  . 
secondary  clouds  ....  are  but  little  affected  by  the  electric  field,  .... 

From  this  it  seems  that  Thomson  did  not  regard  these  secondary 
clouds  as  precipitated  upon  water  nuclei  derived  from  the  evaporation 
of  the  fog  particles  of  the  first  cloud. 

In  1902,1  and  more  at  length  in  my  memoir  on  the  structure  of  the 
nucleus, §  I  gave  a  detailed  account  of  the  behavior  of  the  residual  water 
nuclei  and  showed  by  direct  experiment  that  the  merest  trace  of  solute 
in  the  fog  particle  evaporated  left  a  persistent  water  nucleus  behind. 
The  water  nuclei  of  pure  water  seem  by  comparison  to  be  evanescent. 
The  reduction  of  vapor  pressure  due  to  solution  compensated  the  in- 
creased vapor  pressure  due  to  curvature. 

*Phil.  Trans.,  p.  428,  vol.  192,  1889. 
fPhil.  Mag.  (5),  1898,  vol.  46,  p.  528  (cf.  pp.  529  and  531) . 
JPhil.  Mag.  (6),  iv,  pp.  262-269,  1902. 

§Structure  of  the  Nucleus,  Smithsonian  Reports,  No.  1373,  1903,  Washington. 
92 


RESIDUAL  WATER  NUCLEI.  93 

In  1903  J.  J.  Thomson*  gave  a  general  account  of  condensation  nuclei, 
at  the  end  of  which  he  formulates  succinct  reasons  for  the  persistence 
of  water  nuclei,  even  when  derived  from  the  evaporation  of  fog  particles 
of  pure  water.  He  says  "on  the  view  of  the  relation  between  surface 
tension  and  the  thickness  of  water  films,  to  which  Reinold  and  Rucker 
were  led  by  their  experiments  with  very  thin  films,  drops  of  pure  water 
of  a  definite  radius  might  be  in  equilibrium  with  saturated  water  vapor 
even  if  they  were  not  charged,"  a  proposition  which  is  thereafter  proved. 
A  further  deduction  of  J.  J.  Thomson's  which  may  be  of  use  below  is 
that  "the  efficiency  of  an  ion  as  a  nucleus  for  condensation  depends 
upon  the  maximum  size  of  the  aggregation,  while  the  velocity  of  the 
electric  field  depends  upon  the  average  size."  Thus  the  "average  size 

of  a  negative  ion  may  easily  be  less  than  that  of  a  positive  ion, " 

while  the  negative  nucleus  is  larger  than  the  positive,  other  things  being 
equal.  I  may  also  add  that  J.  J.  Thomson  computes  the  radius  of  a  vapor 
nucleus  to  be  io~7/i .  9  cm.,  whereas  the  radius  of  the  ionized  nucleus  is 
io~7/3  .  i,  so  that  the  vapor  nuclei  are  slightly  larger  than  the  ions. 

Furthermore,  Thomson  shows  that  vapor  nuclei  are  probably  aggrega- 
tions of  water  molecules,  and  elsewhere  that  "in  a  space  far  from  satura- 
ted with  water  vapor,  ....  drops  will  be  formed,  and  that  the  size  of 
these  drops  diminishes  only  very  slowly  as  the  quantity  of  water  vapor 
in  the  surrounding  air  diminishes  .  .  .  . " 

In  1905  the  Transactions  of  the  St.  Louis  International  Electrical 
Congress  were  published,  which  gave  a  review  of  the  present  state  of  our 
knowledge  of  condensation  nuclei  by  C.  T.  R.  Wilson,  f  This  contains 
the  most  recent  contributions  relating  to  water  nuclei.  In  view  of  the 
investigations  of  Langevin  and  of  E.  BlochJ  on  the  occurrence  and 
behavior  of  slow-moving  ions,  Wilson  finally  summarizes  the  results 
bearing  on  nuclei  as  follows: 

(i)  The  ions  proper,  requiring  a  fourfold  or  sixfold  supersaturation  to  cause  water 
to  condense  on  them,  and  having  a  mobility  exceeding  i  cm.  per  second  in  a  field  of 
one  volt  per  second.  (2)  Loaded  ions,  requiring  little  or  no  supersaturation  to  make 
water  condense  on  them,  and  having  a  mobility  generally  less  than  a  thousandth 
part  of  that  of  the  ions  proper.  (3)  Uncharged  nuclei,  resembling  the  second  class  and 
requiring  little  or  no  supersaturation  in  order  that  visible  drops  may  form  upon  them. 

59.  Purpose,  plan,  and  method. — My  purpose  in  the  present  paper 
is  to  determine  whether  there  is  any  difference  in  the  sizes  of  residual 
water  nuclei  obtained  in  the  evaporation  of  fog  particles  under  different 
conditions;  for  instance,  whether  the  fog  particles  of  large  coronas 

*Conduction  of  Electricity  through  Gases,  Chapter  VII,  Cambridge,  1903. 
tTrans.   of   International   Electrical   Congress   of    1904,   p.   365    (cf.   p.  378),  St. 
Louis,  1905. 

tRecherchessurlaconductilite^lectriquedel'air,etc.,  Paris,  1904  (quoted  by  Wilson) . 


94  CONDENSATION    OF   VAPOR   AS    INDUCED    BY    NUCLEI    AND    IONS. 

evaporate  to  the  same  nucleus  as  the  fog  particles  of  small  coronas;  or, 
more  pertinently,  whether  the  fog  particles  precipitated  on  ions  evapor- 
ate to  the  same  nucleus  as  the  fog  particles  precipitated  on  the  vapor 
nuclei  of  wet  dust-free  air.  A  number  of  allied  questions  will  be  treated. 
A  variety  of  methods  were  tested,  as  follows: 

I.  The  endeavor  was  made  to   find  if  from  fogs  characterized  by 
identical  coronas  the  number  of  residual  nuclei  was  the  same  after  the 
natural  evaporation  during  subsidence,  no  matter  whether  the  original 
precipitate  occurred  on  ions  or  on  the  vapor  nuclei  of  dust-free  air. 

II.  Identical  coronas  were  produced  on  ions  and  on  vapor  nuclei, 
respectively;    but  the  evaporation  of  fog  particles  was  accelerated  by 
keeping  the  influx  valve  open  by  a  definite  amount.     The  number  of 
residual  nuclei  was  then  tested  by  a  second  exhaustion,  the  amount  of 
which  was  varied.    This  was  done  both  by  starting  with  different  press- 
ures in  the  vacuum  chamber  for  full  barometric  pressure  in  the  fog 
chamber  and  by  starting  with  different  partial  exhaustions  in  the  fog 
chamber  for  the  same  pressure  in  the  vacuum  chamber. 

III.  The  persistence  of  the  residual  nuclei  was  studied  by  measuring 
their  decrease  in  number  in  the  lapse  of  time.    Incidentally  the  loss  due 
to  evaporation  was  estimated  and  the  distribution  of  sizes  considered. 
Finally,  in  the  second  part  of  this  chapter  the  method  of  successive 
exhaustion,  which  is  found  to  be  most  productive,  is  brought  to  a  definite 
conclusion. 

In  all  cases  the  ions  were  produced  by  a  weak  sample  of  radium  in  a 
sealed  aluminum  tube,  attached  to  the  top  of  the  fog  chamber.  This 
was  removed  during  the  examination  for  water  nuclei,  inasmuch  as  the 
ions  are  efficient  in  the  presence  of  the  latter.  The  corona  obtained 
from  the  radium  was  always  the  same,  care  being  taken  to  precipitate  all 
residual  water  nuclei  in  these  cases,  and  to  have  a  pressure  difference 
sufficiently  high  to  catch  all  the  ions,  or  at  least  the  same  fraction  of  the 
total  number.  To  produce  the  same  given  corona  with  the  vapor  nuclei 
of  dust-free  air  is  easily  accomplished  after  a  short  preliminary  trial. 
Moreover,  these  coronas  may  be  obtained  at  the  same  pressure  when- 
ever the  asymptote  for  the  ions  has  been  reached.  The  eye  is  always 
40  cm.  and  the  source  of  light  250  cm.  from  the  axis  of  the  fog  chamber. 

60.  Residual  water  nuclei  after  the  natural  evaporation  of  fog  par= 
tides. — The  results  obtained  from  these  experiments  are  given  in  table  40. 
Here  £  =  76  and  p — dp'a  are  the  initial  pressures  of  the  fog  and  vacuum 
chambers;  p — dpa  the  final  pressure,  when  in  communication  after 
exhaustion;  sa/$o  the  angular  diameter  of  the  corona,  observed  for 
ions  and  vapor  nuclei  in  dust-free  air,  as  specified.  Again,  p  =  dpfb', 
p — dpb  denotes  the  initial  pressure  of  the  fog  chamber  and  vacuum 
chamber  before  exhaustion;  p — dpc  the  final  common  pressure  after 


RESIDUAL  WATER  NUCLEI. 


95 


exhaustion,  when  the  fog  particles  corresponding  to  sa  have  subsided, 
leaving  (by  natural  evaporation)  the  residual  water  nuclei  corresponding 
to  the  corona  of  any  diameter  5^/30,  behind. 

40. — Experiments  with  residual  water  nuclei.     Bar.  76  cm.;  temp.  14°  C. 
Natural  evaporation. 


Precipitation  on  — 

dp'a. 

Spa. 

Jo. 

( 

*/>«//>. 

WaXlO"3 

' 

*v 

Vapor  nuclei  

28  •* 

26    7 

3c 

^ 

>      "*  ^1 

Rad  ions 

29.3 
29-3 

2Q    "3 

27-5 
27.8 
07    7 

'6.9 

26-9 
IA  Q 

'•  oo1 

.385 
.385 

-jOc 

1  06 
1  06 
infi 

*  1  •  0 

27;8 

u.  y 

•  o°o 

27  •  7 

Precipitation  on  — 

*. 

dpc. 

V 

dp     c 

p~ 

'Pc-dph 

11 

bX  io~*. 

Vapor  nuclei  

26  s 

2    'I 

o 

•j  An 

^  6 

Rad  ions 

II-  9 

no 

26.8 
26    7 

2-7 

3Q 

.232 
211 

4.2 
c  6 

•  *JL 

0  -u 

xwo;     2gbp. 

Table  40  shows  that  for  initial  coronas  of  the  same  size,  5  =  6.9,  "the 
residual  coronas  5  =  2.7  and  3.0  do  not  differ  sufficiently  to  make  the 
evidence  decisive.  Less  than  one-tenth  the  original  number  of  ions  are 
represented  by  water  nuclei,  the  remainder  having  vanished  by  sub- 
sidence with  the  fog  particles  or  otherwise.  There  does  not  seem  to  be 
any  certain  difference  between  the  behavior  of  vapor  nuclei  and  of  ions, 
so  far  as  these  experiments  go.  The  large  number  surviving  in  the  first 
instance  (small  initial  corona),  as  compared  with  a  smaller  number  in 
larger  coronas,  is  striking. 

61.  Rapid  evaporation  of  fog=particles. — In  table  41  the  filter  cock 
is  left  slightly  open  in  order  that  the  water  nuclei  may  be  increased. 
The  fog-chamber  is  initially  at  barometric  pressure.  The  initial  pressures 
of  the  vacuum  chamber  are  ^  =  76.7 — 23.6  cm.,  to  catch  the  ions 
produced  by  weak  radium  and  numbering  about  100,000.  The  pressure- 
differences  are  then  reduced  successively  to  the  values  to  catch  the  water 
nuclei  left  after  the  accelerated  evaporation  specified.  The  exhaustion 
drops  from  p  and  p — dp'  as  initial  pressures  in  fog  chamber  and  in 
vacuum  chamber  to  p—dp3,  the  final  common  pressure  in  both,  while 
°°  —  dpzlP  is  a  convenient  datum  for  the  comparison  of  the  water  nuclea- 
tions  n.  These  have  been  corrected  for  the  temperature  /  of  the  fog 
chamber,  more  water  being  precipitated  as  /  is  higher  and  for  volume 
expansion  from  v  at  /  to  vl  at  /r 


CONDENSATION  OF  VAPOR  AS  INDUCED  BY  NUCLEI  AND  IONS. 


TABLB4L — Sizes  of  water  nuclei.    Radium  ionizer.    Slightly  open  filter  cock ; 

t  several  minutes. 


9?. 

9P+ 

sa. 

dPz/P- 

Wlfj. 

m'l). 

w2Xio~3. 

At  20°. 

w2Xio~3. 

Ions  originally  ;j=  7.0  (w  o);  n=  115,000.  Bar.  76.7  cm.;  £'  =  53.  i  cm.;  temp.  2i.o°C. 

I. 

23-6 

22.2 

4-5 

0.289 

30.2 

3i 

23-6 

22.2 

l5-o 

.289 

.... 

40-3 

'4i 

23-6 

22.2 

24-4 

.289 

.... 

28.7 

*29 

23-6 

22.2 

4.6 

.289 

32.1 

33 

13.0 

12.4 

35-4 

.162 

27.8 

28 

16.7 

16.0 

45-2 

.  209 

32.5 

33 

17.0 

16.2 

45-2 

.  211 

32-8 

33 

6.0 

5-9 

67-i 

.077 

30.2 

3i 

23-6 

22.2 

4-7 

.289 

34-4 

35 

23-6 

22.2 

45-5 

.289 

.... 

54-2 

55 

Ions.  .  . 

22  .  2 

7   O 

28Q 

1  14.    7 

117 

Bar.  75.9  cm.;   temp.  26°  C.    Original  corona,  .9  =  6.4;   ^  =  95,000;    dp'  =  22.i  cm. 

II. 

5-0 

4-9 

57-5 

0.065 

30.3 

32 

1-9 

i-9 

«9.2 

.025 

.... 

23.1 

24 

22.1 

20.8 

36-4 

.214 

.... 

83.5 

95 

Ions  .  .  . 

10.3 

10.  0 

35-4 

.132 

22.5 

24 

Bar.  76.2  cm.;    temp.  25.5°  C.;   ions,  n=  115,000. 

III. 

I  .O 

I.O 

78.6 

0.013 

9-5 

IO.  I 

18.0 

17.0 

3-3 

.223 

9-2 

7io-3 

.... 

2.2 

87-5 

.029 

.... 

13.0 

13-8 

.... 

22.1 

2.2 

.290 

.... 

3-6 

74-i 

.... 

1.9 

87-5 

.025 

.... 

12.3 

13.0 

.... 

17.0 

2.8 

•223 

.... 

5-5 

76.2 

3-o 

7-5 

•039 

.... 

18.3 

19.4 

22.  2 

2.  2 

.291 

3-6 

74-i 

Radium  not  removed.  2Cock  open  late.  3gbp.  4wo. 

Subsequent  exhaustion  to  catch  the  water  nuclei  left  after  first  exhaustion. 
«gbp. 


sgyo.  •Hvc. 

we  to  gbp,  very  faint. 


The  data  are  given  in  fig.  30,  w  in  terms  of  the  relative  drop  in  pressure, 
x  =  dp3/p.  Though  the  experiments  were  made  with  great  care  and 
apparently  satisfactory,  the  results  are  disappointing;  but  this  is  prob- 
ably to  be  expected  when  the  water  nuclei  are  only  obtainable  by 
evaporations  lasting  as  much  as  a  fraction  of  a  minute,  during  which 
there  must  be  both  subsidence  and  probably  also  a  washing-out  of 
nuclei  by  the  disturbance  produced  during  the  influx  of  air.  In  the  first 
series,  where  there  are  115,000  ions,  not  more  than  30,000  or  40,000  water 
nuclei  (about  one-third),  are  obtainable.  On  opening  the  filter  cock 


RESIDUAL  WATER  NUCLEI. 


97 


wider  and  as  wide  as  permissible  to  insure  filtration,  the  number  of 
water  nuclei  was  increased  to  over  50,000,  or  to  about  one-half  the  num- 
ber of  ions.  In  the  second  series  about  90,000  ions  were 
available,  because  of  the  lower  drop  dp3,  and  less  than  30,000 
were  represented  by  water  nuclei,  again  about  one-third. 


-,140 


FIG.  30. — Number  of  residual  water  nuclei  obtained  from  rapid  evaporation  of  fog 
particles  and  found  at  different  small  adiabatic  drops  of  pressure  dp/p. 

FIG.  31. — Number  of  residual  water  nuclei  obtained  from  rapid  evaporation  of  fog 
particles  in  a  partially  exhausted  fog  chamber  and  caught  at  different  small  adiabatic 
drops  of  pressure  dp/p. 

When  the  drop  dp3  is  as  low  as  2  cm.,  the  number  of  water  nuclei 
is  relatively  small,  though  at  5  cm.  the  maximum  is  already  reached. 
Unfortunately,  therefore,  the  range  of  marked  variation  of  n  lies  below 
a  few  centimeters  of  dp3,  wherefore  the  coronas  are  too  filmy  and  large 
to  admit  of  easy  identification,  unless  a  special  immense  fog  chamber 
is  constructed  for  small  exhaustions.  So  far  as  these  experiments  go, 
however,  the  appearance  is  rather  such  as  recalls  the  distribution  curves 
for  ions  and  for  dust-free  air;  in  other  words,  the  water  nuclei  are  prob- 
ably of  all  sizes  within  certain  limiting  dimensions,  like  the  ions. 

In  the  third  series  of  table  41  the  attempt  is  made  to  further  study 
these  large,  filmy  coronas.  They  may  be  recognized  with  certainty  here 
and  are  throughout  of  the  green-blue-purple  type,  corresponding  to 
about  100,000  nuclei  under  normal  expansions.  At  the  low  exhaustions 
used,  however,  they  correspond  to  10  or  15  thousand  nuclei  per  cubic 


98  CONDENSATION    OF    VAPOR   AS    INDUCED   BY    NUCLEI    AND    IONS. 

centimeter,  since  but  little  water  is  precipitated.  In  this  series  a  second 
large  exhaustion  was  made  to  catch  the  nuclei  left  by  the  first  exhaus- 
tion in  each  of  the  four  cases.  But  few  nuclei  were  found,  however, 
perhaps  because  considerable  time  (5  minutes)  was  needed  between  the 
exhaustions;  but  the  reason  for  this  is  not  clear.  One  may  notice  in 
conclusion  that  the  numbers  found  for  the  nucleation  depend  essentially 
upon  computation,  as  the  coronas  are  large.  There  is  one  correction, 
m/m27,  to  allow  for  the  small  quantity  of  water  precipitated;  another 
for  the  volume  increase  on  exhaustion;  a  third  for  temperature,  etc. 
The  coronas  themselves  naturally  increase  as  the  expansion  is  larger, 
but  they  do  not  keep  pace  with  the  corrections. 

62.  Continued. — In  the  experiments  of  table  42  the  filter  cock  was 
again  left  slightly  open;  but  the  vacuum  chamber  was  kept  at  the 
same  initial  pressure  p — dp'.  The  low  drops  of  pressure  were  secured  by 
successively  reducing  the  pressure  of  the  fog  chamber,  as  shown  under 
P — ®P a-  This  is  a  much  more  convenient  method  of  experiment,  though 
the  computation  is  more  troublesome.  The  final  common  pressure  after 
exhaustion  is  p  — dp3.  All  other  data  have  the  same  meaning  as  before 
and  corrections  are  added  for  the  precipitation  of  water,  m' /m\  for  the 
volume  expansion  vl/v  and  for  temperature.  The  table  contains  six 
series  of  results  for  different  exhaustions  and  differently  opened  filter 
cock.  Data  are  reproduced  in  fig.  31. 

Naturally  the  same  evaporation  difficulties  are  again  obtained,  but 
the  curves  as  a  whole  are  more  definite.  In  series  I  and  II  the  number 
of  ions  which  survive  in  the  water  nuclei  is  again  about  a  third  in  each 
case;  but  if  the  filter  cock  is  opened  wider,  about  half  as  many  water 
nuclei  occur  relatively  to  the  original  number  of  ions.  If  radium  is  left 
in  place  (series  III,  VI)  the  ions  are  still  efficient  in  presence  of  the 
increased  number  of  nuclei. 

The  curves  corresponding  to  the  distribution  of  water  nuclei  in  series  I 
again  suggest  the  distribution  curve  of  ions  and  of  vapor  nuclei  in  dust- 
free  air.  In  other  words,  all  sizes  of  nuclei  within  a  certain  range  of 
dimension  seem  to  be  present.  Series  II  has  not  been  carried  far  enough, 
for  the  experiment  places  a  lower  limit  at  which  the  method  necessarily 
breaks  down.  Series  VI,  however,  is  of  a  similar  character  to  series  I. 

The  distinctive  feature  of  these  experiments  is  the  occurrence  of 
reduced  nucleation  at  very  much  higher  drops  of  pressure  than  above. 
One  would  naturally  associate  this  with  the  fact  that  the  water  nuclei 
are  stored  before  the  precipitation  of  fog  upon  them,  in  a  partially 
exhausted  vessel.  Yet  the  evidence  is  not  clear  on  this  point.  The 
smallest  nucleation  occurs  at  the  lowest  pressure  attainable,  viz,  59.8  to 
61.9;  but  in  series  II  higher  values  of  n  appear  at  62.0  to  62.4  cm.  A 
larger  drop  of  pressure  is  here  applied  adapted  to  catch  the  smaller  nuclei. 


RESIDUAL  WATER  NUCLEI. 
TABLE  42. — Sizes  of  residual  water  nuclei. 


99 


P. 

8  pa. 

*p» 

S2. 

*P*/P- 

P» 

/>'• 

n2Xio~3. 

At  24° 
w2Xio~3. 

I.     Cock  open  30°.    Bar.  76  cm.;   temp.  24.2°  C.;    £'  =  52.4  cm.    Original  ions,1 
•y==6.9;  n=no,ooo. 

76.0 
76.0 

63-9 
64.0 
68.7 
68.8 
59-8 
61  .9 

0.0 
0.0 
12.  I 
12.0 

7-3 
7-2 

16.2 

14.1 

22.  I 
22.2 
22.9 
22.9 
22.9 
22.6 
23.2 
23.2 

4-5 
4-7 
5-5 
5-4 
5-3 

5-2 

5.2 

5-2 

o.  291 

.292 

169 

2.i7o 

.227 
.224 
.117 
.147 

59-9 
53-8 
53-i 
53-i 
53-i 
53-4 
52.8 
52.8 

54-4 



30.4 

34-8 
3i 
29-3 
37-5 
34-8 
17.4 
22.3 

II.     Higher  exhaustions.     Ions,  n=  130,000. 

76.0 
62.0 
67.9 
67.8 
76.0 

o.o 

14.0 

8.1 

8.2 

o.o 

26.3 
26.5 
26.2 
26.2 

25-8 

4-6 

25'3 
25-i 

5-i 
4-5 

0.346 

.  2O2 

.267 
.266 

•339 

49-7 
49-5 
49.8 
49.8 
50.2 

48.9 

38.9 
33-5 
39-3 
39-0 
35-9 

III.     Miscellaneous.     Ions,  n=  137,000. 

Cock  open  60°  .  . 
Cock  open  90°  .  . 
Radium  in  place 
Ions  

76.0 
76.0 
76.0 
76.0 

o.o 
o.o 

0.0 
0.0 

25-9 
25-9 
25-9 
25-9 

5-i 
5-i 
5-6 
7.0 

0.341 
•341 
•341 
•341 

50.1 
50.1 
50.1 
50.1 

48.9 



50.9 
50.9 
67.9 
129.0 

IV.     Bar.  75.  9  cm.;   temp.  26°  C.     ^'=27.1  cm. 

Cock  open  60°.  . 

75-9 
61.1 

o.o 

14.8 

25-7 
26.5 

5-3 
6.0 

0-339 
.191 

50.2 
49-4 

48.8 

57 
46 

60 
47 

V.     Low  pressure.     dp  =  22.i  cm.     Original  corona,  s  =  6  .  4  ;  n  =  86,ooo. 

75-9 
64.7 
64.0 

o.o 

II  .  2 
II.9 

20.7 
21.5 
21.5 

I5'3 

I5'2 
35-2 

0.273 

•159 
.150 

55-2 
54-4 
54-4 

53-8 

45 
24 
23 

47 
86 
81 

VI.     Bar.  76.0  cm.  ;  temp.  14°  C.    Original  corona  on  radium  ions,  5  =  6.9; 
n  =  97,000.     Cock  open  30°.    ££'  =  27.5  cm. 

Radium  in  place 
Ions  

60.6 

55-9 
76.0 
76.0 

15-4 
2O.  I 
0.0 
0.0 

26.8 
26.9 
25-7 
25-7 

6.2 

5-6 
6.5 
6-9 

0.188 

.  122 

•338 
.338 

49-2 
49.1 
50.3 
50.3 

48.5 

5i-5 
24.9 
108 
127 

42 

21 
82 

97 

i  Loss  by  subsidence.  2  w  o. 


»gbp. 


100        CONDENSATION    OF   VAPOR   AS    INDUCED   BY    NUCLEI    AND   IONS. 
TABLE  42. — Sizes  of  residual  water  nuclei — Continued. 


P. 

dpa. 

*/»,. 

S2. 

dp3/p. 

P» 

P'- 

M2X  io-3. 

At  24° 
w2Xio~3. 

VII.     Bar.  75.7  cm.;   temp.  29.5°  C. 

Ions  

75-7 
75-7 
75-7 
58.2 
58.8 
75-7 

O.O 
0.0 
0.0 

17.5 

16.9 

0.0 

28.1 
27.1 
27.4 
28.0 
28.0 
27.4 

6-9 

16.2 

24-3 

4-7 
4-7 
4-4 

0.371 
•358 
.362 
.  180 
.189 
.362 

47-6 
48.6 
48.3 
47-7 
47-7 
48.3 

46.7 

141 

6I02 

634-5 
20.9 

22.  2 
36.8 

159 

"5 

39 
23 
24 
42 

VIII.     Same.     Lower  pressures.    Bar.  75.  7  cm.;  temp.  29.  5°  C. 

(Ions)    . 

75-7 
53-8 
75-7 
64.0 
53-6 
75-7 

0.0 

21.9 

0.0 

11.7 

22.  I 
0.0 

34-4 
35-2 

34-4 
35-1 
35-5 
34-4 

4.8 
5-0 
4.6 
5-o 
5-6 
6.9 

0.454 

.247 

•454 
.366 
.250 
•455 

41-3 
40-5 
41-3 
40.6 
40.2 

39  3 

59-7 
34-3 
52.6 
52.0 
49.1 
176 

68 
38 
60 
59 
54 

201 

1  Radium  in  place;  ions  active  in  presence  of  water  nuclei. 


2  Radium  off. 


When  the  relatively  large  nuclei  are  caught  at  the  very  low  drop 
of  pressure,  a  higher  drop  applied  in  turn  always  reveals  a  relatively 
large  number  of  water  nuclei,  apparently  too  small  to  have  been  caugftt 
in  the  first  exhaustion.  This  evidence  must  also  be  used  with  caution, 
because  evaporation  in  the  filmy  coronas,  observed  in  the  first  instance, 
is  liable  to  be  a  marked  feature. 

If  the  graphs  of  fig.  31  be  prolonged  until  they  intersect  the  axis  at 
about  #  =  0.05,  the  limiting  superior  diameter  of  water  nuclei  may  be 
estimated  from  the  Kelvin-Helmholtz  equation.  Regarding  the  super- 
saturation  to  be  about  5  =  1.15,  the  amount  of  adiabatic  cooling  as  far 
as  9°,  the  maximum  diameter  for  the  present  series  would  be  about 
d  =  2  X  io~6  cm.  In  the  above  cases  where  the  condensation  began  below 
2  cm.  (say  at  about  i  cm.)  the  maximum  diameter  than  d  =  25  X  io~6  cm. 

One  may  notice,  however,  that  the  effect  of  temperature  enters  abso- 
lutely into  Helmholtz's  equation,  so  that  if  the  minimum  volume  of 
expansion  could  be  found  it  would  be  worth  while  to  compute  d  carefully. 
S  decreasing  rapidly  implies  a  corresponding  rapid  increase  of  d. 

In  series  VII  and  VIII,  made  at  a  somewhat  later  date,  high  exhaus- 
tion and  (incidentally)  relatively  high  temperatures  occur.  The  data  are 
also  given  in  fig.  2,  but  they  show  no  definite  tendency.  There  remain 
for  discussion  series  IV  and  V,  in  each  of  which  the  filter  cock  was  open 
as  widely  as  permissible  and  in  which  the  number  of  water  nuclei  result- 
ing from  more  rapid  evaporation  is  often  twice  as  large  as  heretofore. 
In  each  of  these  cases  the  nucleation  decreases  very  definitely  and 
rapidly  with  the  exhaustion,  as  the  numbers  of  nuclei  were  not  only 
large,  but  their  sizes  distributed  over  a  wide  range  of  values. 


RESIDUAL  WATER  NUCLEI. 


101 


The  values  of  table  42  refer  to  different  numbers  of  initial  ions.  The 
initial  coronas  are  usually  the  same  (w  y  o) ;  but  being  obtained  at 
different  exhaustions,  this  corona  implies  greater  nucleation  as  the 
exhaustion  is  higher.  The  number  of  ions  in  the  tables  has  been  com- 
puted by  supposing  the  exhaustion  to  be  faster  than  the  reproduction  of 
ions;  i.  e.,  the  number  of  ions  found  for  the  exhausted  vessel  is  always 
multiplied  by  the  volume  expansion,  apart  from  the  correction  for  the 
increased  quantity  of  water  precipitated.  It  may  be  questioned  whether 
this  hypothesis  is  justified,  but  there  is  no  way  of  testing  it.  It  is  also 
very  difficult  to  understand  why  the  corona  remains  constant,  while  the 
exhaustion,  after  all  ions  are  caught,  continually  increases  over  enormous 
ranges. 

In  table  43  the  data  of  table  42  are  summarized,  but  without  referring 
them  to  the  same  initial  ionization,  as  these  reductions  would  be  uncer- 
tain. X  =  dp3/p.  Notwithstanding  the  care  given  the  work,  the  results 
are  far  from  satisfactory.  All  series  show,  however,  that  the  number  of 
residual  water  nuclei  present  after  the  evaporation  of  a  fog  originally 
containing  about  100,000  ions  per  cubic  centimeter  is  smaller  as  the 
exhaustion  is  smaller,  as  if  the  water  nuclei  within  certain  ranges  were  of 
all  sizes. 

43. — Summary  of  table  42.     Filter  cock  open  30°.    Data  referred  to  125,00x3 
ions,  originally  present. 


XX  io-3. 

nX  io-3. 

XXio-8. 

«Xio-3. 

Series  I.    Ions  110,000.    Bar.  76.0 
cm.;  temp.  24°  C.;  £'  =  52.  4  cm. 

Series  VI.1  Ions  97,000.    Bar.  76cm.; 
temp.  14°  C.;  £'  =  48.  5  cm. 

291 
292 
169 
170 
227 
224 
117 
H7 

30 
35 
3i 
29 

37 
35 
17 

22 

188 

122 

42 

21 

Series  VII.    Ions  160,000.    Ear.  75.  7 
cm.;  temp.  30°  C.;  £'  =  46.  7  cm. 

362 
1  80 
189 
362 

39 
23 
24 
42 

Series  II.    Ions  130,000.    Bar.  76 
cm.;  temp.  24°  C.;  £'  =  48.  9  cm. 

Series  VIII.  Ions  200,000.  Bar.  75.7 
cm.;  temp.  30°  C.;  £'  =  39.  3  cm. 

346 
1  86 

202 

267 
266 

339 

39 
45 
33 
39 
39 
36 

454 

247 

454 
366 
250 

68 
38 
60 
59 
54 

iMade  at  an  earlier  date.     The  filter  cock  may  have  been  too  widely  open. 


102 


CONDENSATION   OF  VAPOR  AS   INDUCED  BY   NUCLEI   AND   IONS. 


The  effect  of  the  low  pressure  under  which  the  water  nuclei  are  stored 
does  not  clearly  appear;  nor  can  the  effect  of  temperature  be  stated. 
The  most  consistent  results  are  those  of  series  I,  in  which  the  lowest 
exhaustions  were  applied.  One-third  to  one-half  of  the  original  ions 
or  vapor  nuclei  are  represented  by  the  residual  water  nuclei,  the  number 
TABLE  44. — Decay  of  residual  water  nuclei. 


Exciter. 

dp3  and 

tpjp. 

s. 

wXio-3. 

t. 

dps  and 
*PJP. 

sf. 

W'XIO-3. 

Ratio. 

I.  Bar.  76.2  cm.;    temp.  15°  C.;    radium  and  water  nuclei,  £>/>'  =  24.0  cm.;   vapor 

nuclei,  dp'  =  29.  3  cm.;    dp/p  =  0.297  and  0.362;    vl/'v=  1.284  and  1-375  1 

not  corrected  for  temperature. 

Radium.  . 

22.6 

6-9 

86 

90 

22.6 

4.6 

26 

0.30 

dp/p  =  0.297 

86 

90 

.297 

5-o 

32 

-37 

86 

1  80 

.... 

5-o 

32 

•37 

86 

1  80 

.... 

5-o 

32 

•37 

86 

300 

.... 

3-7 

14 

.16 

86 

600 

3-9 

16 

•19 

II.  Wet  air. 

None  

27.6 

17   ? 

I  SO 

1  20 

22    6 

C     T. 

•*8 

O    2S 

0.362 

26.2 

88 

1  80 

•297 

4-2 

20 

•23 

36.9 

117 

300 

5-i 

34 

•29 

36.9 

117 

600 

4.8 

29 

•25 

III.  Repeated.     Identical  pressures  (<?/>'  =  28.  3  cm.)  throughout.    Always  same 
rate  of  influx  (partially  open  cock).    Temp.  22°  C.;  bar.  76  cm.;  vj-v  — 

1-363- 

None  

26.9 

6-3 

9i 

600 

26.9 

4-2 

27 

0.30 

Radium  .  . 

•354 

6-4 

94 

600 

•354 

46-3 

(9i) 

•97 

6.6 

102 

600 

3-6 

17 

•17 

IV.  Repeated.     Bar.  75.2  cm.;    temp.  19°  C.;  vjv=i  .362;  dp'  =  28.3  cm. 

None  

(26.5 

\       -352 

h. 

107 

660 

f  26.5 
I      -352 

J3, 

H 

0.13 

None  

(26.7 
I       -355 

}36-9 

116 

720 

(26.7 

I      -355 

}  3-5 

16 

.14 

Radium  .  . 

86.7 

107 

600 

3-5 

16 

•15 

Radium  .  . 

6.6 

IO2 

600 

3-3 

J3 

•13 

None  

'6.9 

116 

690 

3-8 

20 

.18 

Jgbp.  2wr.  3wog.  4Radium  in  place. 

increasing  with  the  rapidity  of  evaporation.  As  the  evaporation  is 
accentuated,  the  graduation  of  sizes  lies  within  larger  ranges.  Ions  are 
efficient  in  the  presence  of  water  nuclei,  indicating  the  small  bulk  of  the 
latter. 


RESIDUAL  WATER  NUCLEI. 


103 


63.  Persistence  of  water  nuclei.— If  there  is  a  difference  between 
the  water  nuclei  obtained  after  evaporation  of  fog  particles  precipitated 
upon  ions  and  those  precipitated  upon  vapor  nuclei,  this  should  show 
itself  in  a  corresponding  difference  in  the  length  of  life  of  the  types  of 
water  nuclei  in  the  two  cases.  Incidentally  the  number  of  nuclei  dissi- 
pated upon  evaporation  must  appear  in  the  graphs. 

The  data  of  the  experiments  are  given  in  table  44,  where  n  shows  the 
number  of  nuclei  in  the  original  fog  precipitated  upon  ions  or  on  vapor 
nuclei  and  n'  the  number  of  residual  water  nuclei  after  the  evaporation 
of  the  first  fog.  In  series  I  the  filter  cock  was  open  after  the  measurement 
of  the  first  corona  and  the  exhaustion  used  in  the  precipitation  upon  vapor 


0  100         0.00        300        400         SOO        600         100        800 

FIG.  32. — (a)  Persistence  of  residual  water  nuclei  obtained  from  the  evaporation  of 
fog  particles  precipitated  upon  ions  and  vapor  nuclei.  The  curve  shows  the  number 
n  of  water  nuclei  left  t  seconds  after  evaporation.  (6)  Comparison  of  water  nuclei 
obtained  from  evaporation  of  fog  particles  precipitated  upon  phosphorus  nuclei  and 
ions,  in  successive  identical  exhaustions.  (Note  the  conspicuous  loss  in  evaporation 
between  the  first  and  second  precipitations.) 

nuclei  was  greater  than  it  was  in  the  corresponding  case  for  ions.  These 
objectionable  features  were  removed  in  the  second  and  third  series,  where 
identical  exhaustions  occur  throughout  and  the  graduated  filter  cock  (fine 
screw-valve)  was  opened  to  a  definite  number  of  degrees  (30°).  After 
about  60°  the  resistance  of  the  long  filter  prohibited  a  more  rapid  influx. 
The  results  are  all  shown  in  fig.  32,  a,  with  the  series  suitably  dis- 
tinguished by  crosses,  and  they  are  referred  throughout  to  an  initial 
nucleation  of  86,000  per  cubic  centimeter.  The  data  show,  in  the  first 
place,  that  somewhat  more  than  one-third  of  the  original  number  of 
ions  or  of  vapor  nuclei  are  represented  by  these  residual  water  nuclei, 


104          CONDENSATION   OF  VAPOR  AS   INDUCED   BY   NUCLEI   AND   IONS. 

the  remainder  having  been  dissipated  during  the  first  evaporation.  This 
agrees  with  the  above  results.  The  loss  of  nuclei  in  the  lapse  of  time  is 
thereafter  relatively  slow,  not  more  than  one-half  vanishing  in  the 
ensuing  10  minutes.  From  the  nature  of  the  experiments  it  is  idle  to 
endeavor  to  make  out  a  numerical  value  for  the  rates,  but  they  are  of 
the  value  of  those  obtained  on  shaking  very  dilute  solutions,  for  instance. 
Under  the  influence  of  radium,  about  the  same  number  of  water 
nuclei  occur  after  10  minutes,  no  matter  whether  the  initial  dp3  is  26.  7 
or  22.6.  Temperature  corrections  would  not  modify  the  conclusions 
drawn.  When  the  fog  is  precipitated  under  the  same  exhaustions  with 
identically  initial  coronas  (this  is  possible  because  the  vapor  nuclei  are 
efficient  in  the  presence  of  the  ions),  on  either  ions  or  vapor  nuclei,  the 
persistence  of  the  water  nuclei  obtained  on  identical  evaporation  is 
about  the  same.  From  this  one  may  argue  that  the  water  nuclei  which 
persist,  cat.  par.,  are  roughly  independent  of  the  nature  of  the  original 
nuclei.  Finally  in  fig.  32,6,  the  persistence  of  water  nuclei  in  successive 
exhaustions  is  shown  for  comparison,  the  data  being  anticipated  from 
the  next  section.  Water  nuclei  precipitated  on  ions  vanish  much  more 
rapidly  than  for  the  corresponding  case  of  phosphorus  nuclei. 

64.  Summary. — Fogs  when  characterized  by  identical  initial  coronas 
evaporate  naturally,  or  under  compression,  to  about  the  same  number  of 
residual  water  nuclei,  no  matter  whether  the  precipitation  takes  place 
on  ions  or  on  vapor  nuclei.  The  method,  however,  is  rough.  In  the  most 
favorable  cases  about  one-half  of  the  original  number  of  ions  are  repre- 
sented by  the  residual  number  of  water  nuclei.  If  the  drop  of  pressure  is 
continually  decreased  the  number  of  residual  water  nuclei  caught 
decreases  with  the  pressure,  rapidly  below  dp/p  =  o.i  to  0.2.  In  view 
of  the  small  amount  of  water  precipitated  and  of  the  extremely  filmy 
coronas  obtained  as  a  consequence,  measurement  is  difficult.  There  is  a 
lower  limit  to  which  the  drop  of  pressure  may  be  reduced  unless  a  huge 
fog  chamber  is  constructed  specially  for  these  experiments.  For  small 
exhaustions,  coronas  are  liable  to  remain  of  the  same  type  even  though 
dp Ip  decreases  over  wide  ranges. 

The  persistence  of  residual  water  nuclei  is  not  appreciably  different 
when  this  precipitation  of  fog  particles  to  be  evaporated  takes  place  on 
ions  or  on  water  nuclei.  It  is,  however,  enormously  different,  c&t.  par., 
from  the  case  of  phosphorus  nuclei.  It  appears  that  this  difference  is 
not  of  the  nature  of  a  time  loss,  but  of  a  true  evaporation  loss.  When 
water  nuclei  are  obtained  from  fog  particles  precipitated  upon  ions  or 
upon  vapor  nuclei,  the  chief  loss  of  water  nuclei  accompanies  each 
evaporation  of  the  fog  particles,  and  over  one-half  of  the  total  number 
of  ions  may  fail  of  representation  in  the  number  the  nuclei  present  after 
the  first  evaporation.  This  incidental  observation  will  be  systemat- 
ically considered  in  the  next  section. 


RESIDUAL  WATER  NUCLEI. 


105 


THE  PERSISTENCE  OF  WATER  NUCLEI  IN  SUCCESSIVE  EXHAUSTIONS. 

65.  Standardization  with  ions. — A  curious  behavior  appeared  in  an 
attempt  to  standardize  the  coronas  by  aid  of  the  ions  due  to  gamma 
rays  penetrating  the  fog  chamber.  These  were  obtained  from  a  sealed 
sample  of  radium  of  strength  io,oooX  and  weighing  100  mg.  The  coronas 
were  produced  by  successive  exhaustions  of  the  same  value,  the  fogs 
being  dissipated  by  evaporation  as  soon  as  possible.  The  data  given 
in  the  above  way  in  table  45  show  an  enormously  rapid  initial  loss.  To 
obtain  large  coronas,  the  exhaustion  to  catch  the  ions  was  higher  (drop 
of  pressure  dp3  =  22  . 6)  than  to  catch  the  water  nuclei  resulting  from  the 
evaporation  of  fog  particles  (^3  =  17.1).  Hence,  in  the  two  cases 
dp3/p=o.293,  volume  expansion  v1/v  =  i.2&,  and  dp3/p  =  o.22'j,  v1/v  = 
i .  20,  whence  nX  io~3  =  o.  268s3  and  nX  io~3  =  o.  2I5-S3. 


FIG.  33. — Residual  water  nuclei  obtained  from  evaporation  of  fog  particles  precipitated 
upon  ions.  Curve  (a)  shows  number  of  nuclei  computed  and  observed  found  in 
successive  identical  exhaustions;  curve  (6)  the  corresponding  relations  of  nucleation 
n  and  coronal  diameter  s;  (c)  the  corresponding  behavior  of  phosphorus  nuclei 
compared  with  the  ions. 


io6 


CONDENSATION   OF  VAPOR  AS   INDUCED  BY   NUCLEI   AND   IONS. 


The  attempt  to  find  the  subsidence  constant  5  fails;   as,  for  instance, 


,S= 


3-3         2-o         i.o 

12.2  7.9  3.4 


4-4         3-0         i. 
11.5         6.6 


showing  a  well-marked  progression  of  data.  Similarly,  the  attempt  to 
find  n0  in  the  table  fails,  as  the  progression  is  here  equally  manifest.  In 
other  words,  with  the  evaporation  of  the  first  fog  (on  ions)  more  than  half 
the  nuclei  are  lost,  whereas  in  subsequent  evaporations  the  behavior  of 
the  remaining  nuclei  is  more  like  phosphorus  nuclei. 

TABLE  45. — Coronas  standardized.  Ions  from  gamma  rays  (radium).  Bar.  75.  2  cm.; 
temp.  25°  C. ;  90  seconds  between  observations.  Cock  open  5  seconds.  For  ions 
dp'  =  23 . 6  cm. ;  d/>3=22.ocm.;  ^'  =  0.71;  dp3/p  =  o.  293  (factor,  o.268.y3);  forwater 
nuclei,  dp=i8.  i ;  dp^—ij.i',  [dp2]=i6.5;  dp3/p  =  o.22j;  y  =  o. 774.  AssumeS  =  6.5. 


No.  of 
exhaustion. 

Corona. 

s. 

w'Xio-3  = 

0.2I5S3. 

No.  of 
exhaustion. 

Corona. 

s. 

w'Xio~3  = 
0.215-y3. 

(Ions)                i 

w  r 

6  6 

*76    Q 

(Ions)                i 

w  r 

6  6 

*76  Q 

(Water  nuclei)  2 

4-7 

22.3 

(Water  nuclei)  2 

4-4 

18.3 

3 

.... 

3-3 

7-7 

.... 

3-o 

5-8 

4 

.... 

2.0 

i-7 

.... 

1.8 

I  .  2 

5 

.... 

1.0 

0.2 

.... 

0.0 

0.0 

6 

.... 

0.0 

0.0 

These  data  are  shown  in  fig.  33,  where  i o~3n'  =  o.  2 i$s3  indicates  the 
number  of  nuclei  actually  present  in  the  exhausted  fog  chamber  and  n 
the  number  which  presumably  ought  to  be  present.  The  discrepancy  is 
obvious  and  in  large  measure  due  to  the  losses  in  the  first  evaporation. 
Thus,  taking  the  second  residue  (wX  io~3  =  5o.6)  as  the  initial  number 
the  results,  in  thousands  per  cubic  centimeter,  show  that  over  one-half 
are  lost  on  first  exhaustion. 


Nuclei 
present. 

Should  be 
present. 

Nuclei 
present. 

Should  be 
present. 

Ions  

76  Q 

76    Q 

Ions 

76  Q 

76   9 

After  i  evaporation 
After  2  evaporations 
After  3  evaporations 
After  4  evaporations 

22.3 
7-7 
i-7 

0.2 

50.6 

8.0 
0.9 

0.  I 

After  i  evaporation 
After  2  evaporations 
After  3  evaporations 
After  4  evaporations 

18.3 

5-8 

I  .  2 
O.O 

50.6 
6.2 
0.4 
0.0 

The  same  result  may  be  inferred  by  laying  off  the  nucleation  in  terms 
of  the  number  of  the  exhaustion  as  in  fig.  33.  In  fact,  the  phosphorus 
nucleation,  as  taken  from  table  20  for  corresponding  initial  nucleations, 
vanishes  per  exhaustion  more  slowly  throughout. 

66.  Further  data. — Thus  it  appears  that  the  water  nuclei  obtained 
by  evaporating  fog  particles  precipitated  on  ions  vanish  more  rapidly, 
at  least  in  the  beginning,  than  may  be  accounted  for  as  the  combined 
result  of  the  exhaustion  applied  and  the  subsidence.  New  results  were 


RESIDUAL  WATER  NUCLEI. 


I07 


therefore  investigated  in  table  46,  by  aid  of  the  method  of  two  sources, 
5  being  their  distance  apart  on  a  radius  ^  =  250  cm.,  where  S  =  2R 
tan  6/2,  if  6  is  the  angular  diameter  of  the  coronas.  The  number  of 
water  nuclei  must  be  increased  by  the  exhaustion,  but  not  the  initial 
number  of  ions  in  the  exhausted  fog  chamber.  The  data  for  n  are 
taken  from  the  observed  sizes  of  coronas  as  investigated  above. 

TABLE  46. — Fog  chamber  standardized  with  ions  from  radium.    Bar.  76.0  cm.;  temp. 
20°  C.;  60  seconds  between  observations;  subsidence  5  seconds. 


Series  and 
exhaustion  number. 

5. 

o.i2S  =  .y'. 

n  X  io~3 
(exh.). 

wXio-3. 

Calculated 
wXio-3. 

For  ions,  dp'  =  24.0  cm.;   dp3=22.g  cm.;    [d/>2]  =  22.4  cm.    For  water  nuclei, 
dp'  =  24.o  cm.;    dp3=22.g  cm.;    [d£2]  =  22.4  cm.;    d/>3//?  =  0.301;    £=6.5. 

i. 

2.  • 
3- 

(Ions)         i 

gy  72 

39 

27 

21 

y'  17 

72 
42 
30 

21 

18 

y'  70 
40 

29 

20 

8.6 
4-7 

5-2 

2-5 

2.0 

8.6 
5-o 
3-6 

2-5 

2.  2 

8.4 
4.8 

3-5 
2.4 

28 

8-5 
4.1 

2.2 

32 
I3-I 
4.1 
2.9 

29 
12 

3-7 

1  66 
36 
n 

5-3 

2.8 

1  66 

42 
17 

5-3 
3-7 

157 
38 
15 
4.8 

(Water  nuclei)  2 
3 
4 
(Air)                         .  .  5 

(Ions)         i 

(Water  nuclei)  2 

O 

4 
(Air)                          .  .  s 

(Ions)  i 
(Water  nuclei)  2 
3 
4 

The  same.1     For  ions,  ££'  =  24.0  cm.;    dp3=22.g  cm.;    [dp2]  =  22.4  cm.;    dp3/p  = 
0.301.     For  water  nuclei,   ^=18.5  cm.;    ^3=17.7  cm.;    [dp2]=i7.o  cm.; 
^3/^  =  0.233;  ^  =  0.771. 

4- 
5- 
6. 

si   :f 

r  (Ions)       .    .            .1 

71 

47 
33 
24 
14 

0 

72 
40 
30 
20 

13 
o 

72 
42 

33 
25 
15 

0 

8-5 
5-6 
4.0 
2-9 
i-7 

0.0 

8.6 
4.8 
3-6 
2-4 
1.6 

0.0 

8.6 
5-0 
4.0 

3-o 
1.8 
o.o 



162 

45-7 
18.6 

6-3 

1.2 
0.0 

166 
29-3 
13-1 

3-7 

I.O 

0.0 

1  66 
33-6 
17.7 
6-9 
i-4 
o.o 

162 
114 
69 
32 
5-5 
0.9 

1  66 
117 
64 
25 
9 
4 

167 
117 
66 
30 
6-5 
i-4 

(Water  nuclei)  2 
3 

I 

(                                     6 

(Ions)  i 
(Water  nuclei)  2 
3 
4 

6 
(Ions)                          i 

(Water  nuclei)  2 
3 
4 

6 

!Water  nuclei  removed  by  exhaustion,  but  the  ions  are  not. 


108          CONDENSATION   OF  VAPOR  AS   INDUCED  BY  NUCLEI  AND   IONS. 

TABLE  46 — Continued. 


Series  and 
exhaustion  number. 

5. 

o.i2S=.r'. 

wxio-3 
(exh.). 

nx  io-3. 

Calculated 
nx  io~3. 

The  same,  with  ions  from  X-rays.     Bar.  76.1;    temp.  21°  C.     Ions,  ^  =  24  cm.; 
dp3=22.g  cm.;   [^  =  22.4  cm.;    dp3/p  =  o.^oi.    Water  nuclei,  dp'=  18.5  cm.; 
^3=17.  7  cm.;    [<?/>2]=i7.o  cm.;    d/>3//>=o.  233. 

7- 
8. 

9- 

10. 

ii. 

12.  ' 

\  dons}                           i 

O    IO2 
50 
40 
30 
19 
0 
0    102 

54 
4i 
30 
17 

gy  124 

63 
46 

33 
23 
13 
o 

g'  123 
66 

49 
38 
27 
17 
g'  128 
66 
47 
35 
26 

17 

128 

7i 
50 

39 
29 
18 
o 

12.  2 
6.0 

4-8 
3-6 
2-3 
o.o 

12.2 

6-5 
4-9 
3-6 

2.0 
14.9 
7.6 

5-5 
4.0 

2.8 

1.6 
o.o 

14.8 
7-9 
5-9 
4.6 
3-2 

2.0 
15-4 

7-9 
5-6 
4-2 
3-i 

2.0 

15.4 

8.5 
6.0 

4-7 
3-5 

2.O 
O.O 



475 
57 
29 
13 

3-2 

o.o 

475 
74 
30 
13 

2.2 
813 
H5 

44 
17.6 

5-7 
1.9 
o.o 

813 
128 

53 
26 

8.5 

2.2 
IIOO 
128 
46 
20 

8.0 

2.  2 
IIOO 
162 

57 
28 
11.7 

2.8 

o.o 

475 
350 

221 
122 

47 
18 

475 
350 
228 
128 
49 
813 
607 
415 
245 

112 

16 

2 

813 
607 
419 
263 
140 

37 

IIOO 

823 
568 
348 
174 
50 

IIOO 

823 
580 
366 
199 
72 
26 

(Water  nuclei)  2 

3 
4 
5 
6 

i 

2 

3 
4 
5 
(Ions)     i 

(Water  nuclei)  .    ...  2 

3 
4 
5 
6 

7 
(Ions)  i 

(Water  nuclei)  2 
3 
4 

6 

(Ions)                           i 

(Water  nuclei)  2 
3 
4 
5 
6 
dons)                       .    i 

(Water  nuclei)        .   2 

3 
4 
5 
6 

7 

In  the  first,  second,  and  third  series  the  exhaustion  was  somewhat 
above  the  condensation  limit  of  air,  so  that  the  coronas  do  not  vanish. 
But  as  the  vapor  nuclei  are  relatively  inactive  as  compared  with  the 
ions,  the  initial  fall  of  nucleation  is  well  brought  out.  The  exhaustion 
is  here  identical  for  ions  and  for  water  nuclei. 

In  series  4,  5,  and  6  the  exhaustion  for  water  nuclei  is  below  the  con- 
densation limit  of  air  and  the  coronas  vanish  in  successive  partial  evacua- 
tions. It  is  necessary,  therefore,  to  make  the  exhaustion  for  ions  (only) 
above  the  fog  limit  of  air,  as  otherwise  too  few  would  be  caught.  The 
observed  march  of  data  is,  however,  similar  to  the  preceding  experi- 
ments, as  is  shown  in  fig.  34. 


RESIDUAL  WATER  NUCLEI. 


109 


These  results  were  now  varied  by  bringing  to  bear  stronger  radiation 
obtained  from  an  X-ray  bulb  placed  at  successively  decreasing  distances 
D  from  the  fog  chamber.  In  series  7  and  8,  D  =  4o,  in  series  9  and  10, 
D  =  2o  cm.  and  in  series  n  and  12,  D  =  i2  cm.  (about)  from  the  axis  of 
the  fog  chamber.  The  enormous  initial  radiations  drop  off  rapidly  in 
the  same  way  as  in  the  preceding  case.  All  the  series  are  consistent, 
except  the  eleventh,  in  which  the  initial  drop  is  too  large  compared  with 
the  others.  It  was  customary  to  keep  the  exhaust  cock  open  for  5 
seconds,  after  which  the  filter  cock  was  opened  to  dispel  the  fog,  i  minute 
being  allowed  between  the  exhaustions.  The  results  are  shown  in  detail 
in  fig.  34,  a,  b,  c,  together  with  similar  data  for  vapor  nuclei  and  for  phos- 
phorus nuclei. 

TABLE  47. — Vapor  nuclei.     Fog  chamber  standardized. 


Series  and  exhaustion  number. 

5. 

O.I25=/. 

wXio-3. 

Calculated 
nXio-3. 

Bar.  76.0  cm.;    temp.  20°  C.     For  vapor  nuclei,  ^  =  33.1  cm.;    ^3=31.3  cm.; 

[#/?2]  =  30.8  cm.;    ^3/^  =  0.412.     For  water  nuclei,   dp'=i8.$  cm.;    <5/>3=i7-7 

cm.;   [dp2]=i7.o;  dp,/p  =  0.233. 

(Vapor  nuclei)              .    i 

V    1  17 

14.0 

'905 

905 

(Water  nuclei)            ...  2 

j         i 

so 

9.6 

234 

674 

3 

67 

8.0 

135 

482 

4 

52 

6.2 

66 

333 

i  .    < 

5 

39 

4-7 

27.7 

214 

6 

28 

3-4 

10.9 

116 

7 

19 

2-3 

3-3 

39 

8 

10 

I  .  2 

0-3 

13 

(Vapor  nuclei)  i 

y  116 

p  cor     72 

13-9 

8.6 

'905 
1  66 

905 
673 

(Water  nuclei)  2 

3 

r^  ^-               / 

r     61 

7-3 

103 

473 

4 

50 

6.0 

57 

319 

2. 

5 

37 

4-4 

23-7 

20  1 

6 

26 

3-1 

8 

103 

7 

20 

2.4 

3-7 

26 

i                                             8 

IO 

1.2 

0-3 

6 

Bar.  76.  i  cm.;  temp.  21°  C.    For  vapor  nuclei,  ^3=28.3  cm.;  d/>3//>=  i  -233-    For 
water  nuclei,  dp  s/p  —  o.  37  2. 

(Vapor  nuclei)  i 

6.8 

5-2 

8.2 
6.2 

172 
66 

172 

120 

(Water  nuclei)  2 

3 

4.0 

4.8 

29 

77 

3- 

4 

2.7 

3-2 

9.1 

42 

5 

i-7 

2.0 

2.  I 

12 

6 

0.0 

O.O 

0.0 

4 

4- 

(Vapor  nuclei)          .  .  .  .  i 

7-i 
5-i 
4-3 

8.5 
6.1 
5-2 

191 

61 
35 

191 

134 
85 

(Water  nuclei)          ....  2 

3 

4 

3-3 

4.0 

17-7 

49 

5 

2-5 

3-0 

6.9 

22 

1  Water  nuclei  removed  by  exhaustion,  but  not  the  vapor  nuclei. 


110          CONDENSATION   OF  VAPOR  AS   INDUCED   BY  NUCLEI   AND   IONS. 


RESIDUAL  WATER  NUCLEI. 


Ill 


67.  Data  for  vapor  nuclei. — Table  47  contains  similar  data  for  the 
vapor  nuclei  of  wet  dust-free  air.  In  series  i  and  2  large  coronas  or  high 
nucleations  are  met  with  at  the  start,  and  they  are  compared  in  fig. 
34,  c,  with  a  corresponding  case  for  ions.  In  series  3  and  4  lower  initial 
nucleations  are  contained,  and  these  data  are  compared  in  fig.  34  with  the 
corresponding  cases  of  ions  and  phosphorus  nuclei.  Corrections  for 
subsidence  should  have  been  added  to  the  graphs  for  ions  and  for  vapor 
nuclei,  but  these  are  not  large  enough  to  modify  them  materially,  so  far 
as  the  figures  go.  ^ 


ZO        40 


60         80 


100 


1ZO        140 


FIG.  35. — Relative  difference  of  nucleation  (nf  —  n)  /n  of  water  nuclei  from  fog  particles 
precipitated  upon  phosphorus  nuclei  and  on  ions,  in  terms  of  i/n.  The  serial  number 
of  the  initial  nucleation  is  attached  to  each  curve. 

68.  Remarks  on  the  tables. — The  graphs  in  figs.  34,  a,  to  34,  c,  show 
unmistakably  that  the  water  nuclei  obtained  from  the  evaporation  of 
fog  particles  precipitated  on  ions  vanish  in  the  successive  exhaustions 
faster  than  in  the  corresponding  case  with  the  vapor  nuclei  of  dust-free 
air;  while  the  water  nuclei  from  fog  particles  precipitated  on  vapor 
nuclei  vanish  much  faster  than  is  the  case  for  the  corresponding  solu- 


112          CONDENSATION   OF  VAPOR  AS   INDUCED   BY  NUCLEI  AND   IONS. 

tional  nuclei  obtained  with  phosphorus  emanation.  It  is  thus  necessary 
to  examine  in  detail  the  three  more  obvious  causes  for  the  decrease  in 
nuclei,  which  are  as  follows:  (i)  The  exhaustions,  applied  alike  in  all 
cases;  (2)  the  subsidence  of  fog  particles  during  the  short  time  of  their 
suspension,  i.  e.,  between  the  exhaustion  and  the  evaporation  by  influx  of 
air;  (3)  the  occurrence  of  electrical  charge  in  the  case  of  ionized  nuclei, 
whereby  the  charged  water  nuclei  may  be  brought  to  coalescence. 

Probably  the  best  method  of  reaching  a  numerical  result  will  consist 
in  eliminating  the  effect  of  exhaustion  and  subsidence,  as  was  done  above 
for  phosphorus  nuclei,  thus  leaving  the  new  losses  of  nuclei  alone  out- 
standing. If 


where  y  is  the  exhaustion  ratio  and  the  product  n(i  —  S/s2,^),  the 
correction  for  subsidence,  the  data  marked  n*  calculated  in  the  table  may 
be  obtained.  They  are  such  as  apply  for  solutional  nuclei  produced  by 
phosphorus,  but  they  are  throughout  enormously  in  excess  of  the  values 
n  observed  for  vapor  nuclei  and  for  ions.  If  we  suppose  that  there  is  a 
second  cause  of  dissipation  with  each  exhaustion  we  may  therefore  write 
(abbreviating  the  products  n) 

n'n**ndf-l&-lTL 

merely  to  get  a  numerical  statement  of  the  case.  The  values  of  the  frac- 
tion or  coefficient  of  survival  x  so  found  show  a  gradual  increase  of  value 
as  the  numbers  of  exhaustions  increase  or  the  nucleations  decrease,  indi- 
cating that  the  greatest  dissipation  of  nuclei  is  during  the  first  exhaustion. 
If  these  values  of  x,  as  summarized  in  table  48,  be  constructed  in 
terms  of  n,  they  show  that  x  is  considerably  in  excess  for  vapor  nuclei 
as  compared  with  ions.  Thus,  at  an  average  (w1  +  w2)/2,  very  roughly, 

I00)000     vapor  nuclei  ions,  <  x    °'^ 
=   50,000     vapor  nuclei  ions,  {  x  =   '  2 


=    10,000    vapor  nuclei  ions,  I  x  =    '  ^ 

results  which  are  too  irregular  for  further  comparison. 

A  simple  term  like  (nf — n)/n  is  preferable  in  other  respects,  and  in 
order  to  put  the  larger  and  more  certain  data  on  the  diagram,  (n' — n)/n 
may  be  constructed  in  terms  of  i  /n.  If  it  were  a  question  of  time  loss 
merely,  some  further  theoretical  progress  might  be  made,  but  the  results 
are  not  sufficiently  smooth  to  give  much  assistance  here.  Hence  in  fig. 
35  •  (n' — n)/n  is  shown  in  terms  of  io6/w,  both  for  ions  and  for  vapor 
nuclei.  In  both  cases  the  curves  rise  higher  as  the  parameter  n  is  greater. 
The  initial  ascent  is  not  very  different  for  ions  and  for  vapor  nuclei. 
The  dissipations  up  to  (or  due  to)  the  first  exhaustion  are  similar  in 
amount.  But  thereafter  the  curves  for  ions  rise  more  rapidly  than  the 


RESIDUAL  WATER  NUCLEI. 


corresponding  curves  for  vapor  nuclei,  showing  that  the  water  nuclei  in 
the  latter  case  are  more  persistent  under  successive  exhaustions  and 
evaporation  than  the  ions. 

TABLE  48. — Summary  of  table  46.    Ions. 


Series. 

Observed 

Computed 
n'  X  io-3. 

IO6/M. 

(„-„,*. 

xXio*. 

x,  x',  x",  etc. 

d'Xio5. 

4- 

162 

162 

6 

0 

.... 

.... 

38 

46 

114 

22 

2.0 

40 

0.40 

57 

19 

69 

54 

3-8 

52 

.68 

80 

6 

32 

159 

5  •  * 

59 

•7i 

no 

i 

6 

830 

4-5 

69 

i  .  i 

190 

5- 

1  66 

166 

6 

o 

37 

29 

117 

34 

3-o 

25 

0.25 

67 

13 

64 

76 

3-9 

45 

.80 

89 

4 

25 

267 

5-7 

53 

•75 

133 

i 

IO 

IOOO 

8-5 

80 

2-7 

200 

6. 

1  66 

167 

6 

0 



37 

34 

117 

30 

2.4 

29 

o.  29 

64 

18 

66 

56 

2.7 

51 

.90 

80 

7 

30 

145 

3-3 

61 

.89 

107 

i 

6 

690 

3-6 

68 

•  9i 

1  80 

7- 

475 

475 

2 

o 

.... 

26 

57 

350 

17 

5  •  J 

16 

o.  16 

53 

29 

221 

34 

6.6 

33 

.69 

67 

13 

122 

77 

8-4 

45 

.84 

89 

3 

47 

312 

14.0 

51 

.80 

140 

8. 

475 

475 

2 

o 

.... 

26 

74 

350 

13 

3-7 

21 

0.21 

49 

30 

228 

33 

6.6 

33 

•52 

65 

13 

128 

77 

8.8 

44 

•77 

89 

2 

49 

450 

46 

•53 

1  60 

9- 

810 

813 

i 

0 

21 

j  j  e 

607 

9 

4-3 

19 

o.  19 

42 

44 

415 

23 

8.4 

48 

•58 

58 

18 

245 

57 

12.5 

52 

•  65 

8O 

6 

112 

175 

18.5 

47 

•  71 

114 

10. 

810 

813 

i 

0 

.... 

22 

128 

607 

8 

3-7 

21 

0.21 

41 

53 

419 

19 

6-9 

51 

.62 

54 

26 

263 

38 

9.1 

56 

.76 

70 

8 

140 

118 

15-4 

50 

.61 

IOO 

n. 

IIOO 

IIOO 

i 

0 

21 

128 

823 

8 

5-4 

16 

o.  16 

41 

46 

568 

22 

11.4 

43 

•  51 

57 

,_/• 

20 

8 

348 

174 

50 
125 

16.4 

21 

49 
46 

*8i 

76 
103 

12. 

IIOO 

IIOO 

I 

O 

21 

162 

823 

6 

4-1 

20 

o.  20 

38 

57 
28 

12 

580 
366 
199 

17 
36 
85 

9-2 

12.  I 

16.0 

46 

53 
49 

•77 
•76 

53 
68 

92 

114          CONDENSATION   OF  VAPOR  AS   INDUCED   BY   NUCLEI   AND   IONS. 
TABLE  48 — Continued. — Summary  of  table  47.     Vapor  nuclei. 


Series. 

Observed 
wXio-3. 

Computed. 
n'Xio-3. 

I06/W. 

(n'-n)/n. 

*Xio2. 

x,  x',  x",  etc. 

dXio5. 

i. 

905 

905 

j 

0.0 

23 

234 

674 

4 

i-9 

35 

0-35 

33 

135 

482 

7 

2.6 

53 

.80 

40 

66 

333 

15 

4.0 

58 

•7i 

52 

28 

214 

36 

6-7 

60 

•65 

68 

ii 

116 

92 

9-5 

-73 

94 

3-3 

39 

300 

ii 

.90 

140 

2. 

905 

905 

i 

o.o 

23 

166 

673 

6 

3-o 

25 

•25 

37 

103 

473 

10 

3-6 

47 

.88 

44 

57 

319 

18 

4.6 

56 

.82 

53 

24 

201 

42 

7.8 

59 

.67 

73 

8 

103 

125 

ii.  9 

•65 

103 

4 

26 

270 

.... 

.... 

i-7 

134 

i 

3- 

172 

172 

6 

0.0 

.... 

.... 

39 

66 

120 

15 

0.8 

55 

0-55 

52 

29 

77 

34 

i-7 

62 

.69 

67 

9 

42 

no 

3-6 

60 

•58 

100 

2 

12 

450 

4.8 

66 

.82 

160 

4- 

191 

IQI 

5 

o.o 

38 

61 

134 

16 

I  .  2 

"46 

0.46 

53 

35 

85 

29 

1.4 

64 

.89 

62 

18 

49 

56 

i-7 

7i 

.88 

80 

7 

22 

145 

2.5 

75 

.86 

107 

Finally,  the  best  method  of  interpreting  the  above  results  is  in  terms 
of  an  equation  of  the  form  (if  nt  be  the  initial  nucleation) 


=  n.<v*-1' 


n 


where  nz  is  the  nucleation  of  the  2th  exhaustion,  y  the  exhaustion  ratio, 
II  the  subsidence  correction,  and  x,  x',  x",  etc.,  the  successive  coefficients 
showing  the  relative  survival  x,  or  the  corresponding  loss  i — x,  of  nuclei, 
accompanying  the  evaporation  of  fog  particles.  This  equation  asserts 
that  the  loss  is  different  in  the  successive  evaporations,  and  this  is 
actually  the  case,  as  has  been  fully  shown  in  table  48.  The  data  x,  x', 
x",  etc.,  have  been  constructed  in  fig.  36,  a,  b,  c,  d,  in  terms  of  the  number 
of  successive  identical  exhaustions  for  the  case  where  the  nuclei  are  ions, 
and  in  fig.  36,  e,  /,  for  the  case  of  vapor  nuclei.  The  ordinates  thus  show 
the  fraction  of  the  total  number  of  fog  particles  evaporated,  surviving  as 
nuclei  after  the  particular  evaporation  given  (in  turn)  by  the  abscissas. 
It  is  not  probable  that  more  than  three  or  four  successive  data  will  be 
trustworthy,  because  with  the  rapidly  decreasing  size  of  coronas  the 
errors  are  cumulative. 

Fig.  36,  a,  b,  c,  d,  shows  that  the  effect  of  the  first  evaporation  is 
always  preponderating  and  that  it  is  more  destructive  as  the  original 


RESIDUAL  WATER  NUCLEI.  lit 

number  of  ions  is  greater.  Thus  when  n  =  160,000,  i—x  or  60  to  70  per 
cent  are  lost  during  the  first,  and  only  about  i—x'  or  20  per  cent  during 
the  second  and  subsequent  evaporations.  If  «  =  900,000  to  1,100,000 
where  the  fog  particles  are  very  much  smaller,  the  first  destroys  about 


•ZO 


FIG.  36,  a,  b,  c,  d  e,  f. — Charts  showing  the  rate  of  survival  of  nuclei  in  each  successive 
identical  evaporation  of  fog  particles  precipitated  upon  ions,  x  is  the  relation  of 
the  number  of  nuclei  after  the  given  evaporation  of  fog  particles  to  the  number  of 
nuclei  before  it.  The  abscissas  show  the  number  of  evaporation  in  the  series. 

80  per  cent,  the  second  40  per  cent,  the  third  30  per  cent  of  the  number 
which  happen  to  be  present  just  before  the  respective  evaporation. 
Hence  for  large  values  of  n  the  loss  due  to  evaporation  is  appreciable 
throughout  many  repetitions. 


n6 


CONDENSATION   OF  VAPOR  AS   INDUCED  BY   NUCLEI   AND  IONS. 


The  results  (fig.  36,  e,  f)  for  fog  particles  precipitated  upon  the  vapor 
nuclei  of  dust-free  air  are  similar,  but  in  no  case  does  the  coefficient  of 
survival  x  increase  after  the  second  exhaustion,  as  was  the  case  with 


40       60       SO       ZO       40       60       80       100 


&0         30         40          SO         40         60         80         100 


FIG.  37,  a,  b,  c,  d,  e. — The  same  as  fig.  36,  showing  x,  x',  x",  in  terms  of  the  diam- 
eters d  of  fog  particles  evaporated. 

ions.  (Compare  fig.  36,  c,  d,  with  fig.  36,  e,  /,  all  of  which  apply  for  high 
original  nucleations  of  about  io6  per  cubic  centimeter.)  Contrasting 
the  case  of  ions  with  the  case  for  vapor  nuclei,  by  comparing  a  with  e 
and  c,  d  with  /,  in  fig.  36,  specifically,  the  coefficient  of  survival  is  always 


RESIDUAL  WATER  NUCLEI.  117 

decidedly  smaller  for  ions  in  the  first  exhaustion  than  for  vapor  nuclei. 
The  charged  nuclei  are  therefore  destroyed  in  greater  number  by  the 
evaporation  of  fog  particles  precipitated  on  them.  When  the  number 
of  nuclei  is  large  (io6)  this  is  also  time  in  subsequent  evaporations,  though 
the  contrast  is  less  marked. 

Another  question  which  comes  up  for  settlement  is  this:  Whether 
the  fog  particles  which  are  represented  by  nuclei  after  evaporation  are 
above  a  certain  critical  size,  and  those  particles  which  vanish  are  below 
it.  This  is  hardly  probable,  because  all  the  fog  particles  contributed  to 
the  same  corona  and  because  it  implies  an  enormous  inequality  in  the 
fog  particles  of  the  first  exhaustion,  considering  that  45  to  85  per  cent 
of  these  vanish  in  the  different  cases  cited.  For  the  present  purpose  it  is 
sufficient  to  write  dsf  =  0.0032,  where  s'  may  be  taken  from  tables  46 
and  47.  These  results  for  the  diameters  of  fog  particles  are  given  in 
table  48.  They  are  constructed  graphically  in  fig.  37,  a,  b,  for  ions,  and 
in  fig.  37,  c,  d,  for  water  nuclei. 

Fig.  37,  a,  containing  series  4  to  8  for  ions  and  small  nucleations  below 
500,000,  suggests  that  x  may  change  abruptly  when  d  —  0.0006  cm.; 
while  fig.  37,6,  for  ions  and  large  nucleations,  io6  has  the  same  appear- 
ance at  d  —  0.0005  cm-  It  is  seen,  however,  that  this  is  nothing  more 
than  the  transition  from  the  first  to  the  second  evaporation,  the  former 
being  so  much  more  efficient. 

"Fig-  37»  c  and  d,  for  large  and  small  nucleations  of  vapor  nuclei,  has 
the  same  character.  In  c,  for  instance,  there  is  an  abrupt  change  below 
40,000  nuclei.  But  the  case  is  again  one  instancing  the  paramount 
importance  of  the  first  evaporation.  There  is,  however,  no  doubt  of  an 
outstanding  effect  due  to  the  number  or  the  size  of  nuclei.  The  co- 
efficient of  survival  x  decreases  as  the  number  of  nuclei  increases,  or 
better,  as  their  size  diminishes.  Thus,  if  the  comparison  be  restricted 
to  the  first  evaporation  fig.  37,  e, 


Ions  .........  /ioM-38     37     37 

I  i  era:  =  40     25     29 


Vapornuclei..(I0^  =     39 
I  io2x=     55 


55     46 


26    26 
16     21 


35     25 


21       22 
19       21 


21     21      centimeters. 
16     20 

centimeters. 


from  which  the  increase  of  x  with  the  size  of  particles  is  put  beyond 
question  and  the  larger  coefficient  of  survival  for  vapor  nuclei  as  com- 
pared with  ions  is  again  apparent.  Whether  the  peculiar  features  of  the 
curve  (fig.  37,  c),  which  reappears  in  each  case,  have  a  definite  meaning 
must  be  left  to  conjecture;  but  in  most  of  the  curves  a,  b,  c,  d,  e,  the 
occurrence  of  maximum  %  is  in  evidence. 

69.  The  loss  of  nuclei  actually  due  to  evaporation.—  It  is  finally  to 
be  shown  that  the  peculiar  loss  of  water  nuclei  resulting  after  evapora- 
tion of  fog  particles  precipitated  upon  ions  is  due  to  this  evaporation 


Il8          CONDENSATION   OF  VAPOR  AS   INDUCED  BY  NUCLEI   AND   IONS. 


(or  its  equivalent)  and  not  due  to  the  dissipation  of  the  water  nuclei  in 
the  lapse  of  time.  It  might  be  supposed,  for  instance,  that  water  nuclei 
obtained  from  the  fog  condensed  on  the  ions  are  smaller  and  therefore 
diffuse  more  rapidly  than  water  nuclei  obtained  by  other  methods. 
If  so,  then  if  the  time  between  the  successive  exhaustions  is  doubled, 
trebled,  etc.,  the  loss  should  be  correspondingly  increased. 

TABLE  49. — Successive  exhaustion  after  different  time  intervals.  Ions  due  to  gamma 
rays.  Bar.  76.1  cm.;  temp.  i8°C.;  dp3=22. 9  cm.  For  ions,  dp3/p  =  o.^oi ;  dpz= 
1 7. 7  cm.  For  water  nuclei,  [dp2]=  1 7.0  cm.;  dpz/p  =  0.232;  -v1/v=i.2i. 


Series. 

Time. 

s. 

Exhausted 

nXio-3. 

Series. 

Time. 

5. 

Exhausted 
wXio-3. 

»X,o-. 

I. 
II. 
III. 

IV. 
V. 

min. 

0 

i 

2 

3 
4 

0 

i 

2 

3 
4 

0 

2 

4 
6 

8 

o 

3 
6 

9 

0 

4 
8 

12 

38 
26 

o 

46 

30 

22 
12 

49 

30 

20 

IO 

J68 
42 
25 
15 

66 

32 

20 
12 

175 

22 

6.6 
1.6 

0.0 

1  66 
36 
ii.  6 
3-8 
0.5 

1  66 

44 
10.8 

0-3 

146 

27 
5-7 

1.2 

129 
12.7 

•5 

175 

27 

8.0 

2.0 
0.0 

166 

44 
14.0 
4.6 
0.6 

1  66 

53 
13.0 

3-7 
0-3 

146 
33 
6.9 

129 
15-4 
3-7 
0.6 

Radium  left  in  place  except  during 
exhaustion. 

VI. 

o 
i 

2 

3 
4 

46 

33 
23 

12 

170 
36 
14.6 
4-7 
0-5 

170 

44 

17.7 

5-7 
0.6 

Bar.,  76  cm.;   temperature  21°  C. 

VII. 
VIII. 

0 

4 
8 

12 
O 

6 

12 

18 

76 
38 
23 
12 

70 

39 

22 
12 

196 

22 

4-7 
0.5 

157 
23 
3-8 
0-5 

196 

27 

5-7 
0.6 

157 
28 
4.6 
0.6 

1  g  to  gy  corona. 

Table  49,  constructed  on  the  above  plan  but  containing  the  time 
interval  /,  in  minutes  between  the  exhaustions,  shows  that  the  time  effect 
is  secondary.  The  table  gives  n  with  correction  for  the  exhaustion  or 
volume  increase  v^/v. 

The  data  are  represented  in  fig.  38,  the  abscissa  being  the  time  in 
minutes,  the  ordinates  showing  the  nucleation.  The  curves  indicate 
a  steady  progression  toward  the  right  as  the  time  interval  increases, 
showing  that  the  time  losses,  although  not  necessarily  absent,  are  not  of 
serious  importance.  In  fact,  in  fig.  39  the  group  for  i -minute  and  6- 
minute  intervals  constructed  in  terms  of  the  number  of  exhaustions 
(ignoring  lapse  of  time)  are  virtually  coincident.  Again,  the  curve  for 


RESIDUAL  WATER  NUCLEI. 


119 


2 -minute  intervals  actually  shows  less  loss  (due  to  favorable  exhaustion 
conditions)  than  the  curve  for  i -minute  interval. 

In  series  6  radium  was  left  in  place  except  during  the  exhaustion, 
(for  ions  are  efficient  in  presence  of  water  nuclei).  It  is  seen,  however, 
that  the  water  nuclei  stored  in  this  ionized  field  do  not  decay  more 
rapidly  than  in  ordinary  dust-free  wet  air. 


180 


ISO 


to 


1Z 


FIG.  38. — Nucleation  of  residual  water  nuclei  in  successive  identical  exhaustions  made 
at  different  intervals  of  time  apart.  Fog  particles  precipitated  upon  ions. 

FIG.  39. — The  same,  constructed  for  successive  exhaustions  and  ignoring  the  time 
intervals. 

All  the  results  might  be  made  more  striking  by  reducing  them  to  the 
same  initial  nucleation  or  ionization.  Just  how  differences  in  these 
values  arise  is  difficult  to  affirm,  but  all  the  after  effects  in  the  successive 
exhaustions  are  usually  consistent.  It  does  not  follow,  however,  that 
the  correction  is  to  be  made  by  proportionately  increasing  all  the  low 
nucleations  by  the  amount  required  in  the  primary  nucleation.  Series 
7  and  8  were  therefore  added  specially  with  a  view  to  normally  large 
initial  nucleations. 


120        CONDENSATION   OF   VAPOR   AS    INDUCED   BY   NUCLEI    AND   IONS. 

70.  Conclusion.  —  When  fog  particles  are  precipitated  upon  solutional 
nuclei,  like  those  of  phosphorus,  the  losses  in  successive  identical  ex- 
haustions are  due  to  the  magnitude  of  this  exhaustion,  to  subsidence, 
and  (in  a  small  measure)  to  time  losses  or  decay. 

On  the  other  hand,  when  fog  particles  are  precipitated  on  ions  or 
vapor  nuclei,  there  is  an  additional  and  usually  very  large  loss,  accom- 
panying the  evaporation  of  the  fog  particles  to  water  nuclei.  Fully  50 
to  80  per  cent  of  the  nuclei  may  be  lost  after  the  first  evaporation.  The 
time  between  the  evaporations  is  of  little  consequence.  More  nuclei  are 
lost  for  the  cases  of  ions  than  for  the  cases  of  vapor  nuclei,  other  things 
being  equal.  All  this  is  very  well  brought  out  by  the  figures. 

The  loss  decreases  as  the  number  of  the  exhaustion  increases,  or  as 
the  number  of  nuclei  present  is  smaller,  or  better,  as  their  size  is  larger. 
If,  apart  from  subsidence,  the  nucleation  nz  of  the  0th  identical  ex- 
haustion of  ratio  y  be  put 


the  fractions  x,  x'  ',  xff,  etc.,  make  an  increasing  series  and  may  be  called 
the  successive  coefficients  of  survival  characteristic  of  the  sizes  of  fog 
particles  in  each  of  the  successive  evaporations.  The  values  of  x  increase 
from  about  o  .  2  for  large  and  o  .  5  for  small  ionization  in  the  initial 
evaporation  to  about  o  .  8  in  the  latter  evaporations.  For  particles  of  like 
size  x  is  larger  for  vapor  nuclei  than  for  ions.  The  x  values  of  the  initial 
evaporation  distinctly  increase  with  the  respective  size  of  particles  in  all 
cases. 


CHAPTER  VI. 
THE  DECAY  OF  IONIZED  NUCLEI  IN  THE  LAPSE  OF  TIME. 

71.  Introduction.  —  The  attempt  was  made  in  an  earlier  paper  to 
standardize  the  coronas  by  aid  of  the  decay  curves  of  radium.  The 
method  is  apparently  very  simple  and  requires  the  knowledge  merely  of 
the  coronas  appearing  under  given  circumstances  when  the  radium  tube 
is  in  place  d  on  the  outside  of  the  fog  chamber,  in  comparison  with  the 
coronas  observed  under  the  same  circumstances  when  the  radium  has 
suddenly  been  removed  for  different  lengths  of  time  before  condensation. 
From  electrical  observations  the  equation 

dn/dl=—bn2         or         i/n  =  i/n'  -\-b(t—  t') 

is  found  to  be  adequate  if  n  and  n'  denote  the  ionizations  occurring  at 
the  times  t  and  t'  ,  and  the  same  would  appear  to  be  the  case  with  the 
corresponding  nucleations.  Moreover,  if  the  relative  nucleations  n'/n  for 
two  coronas  obtained  at  a  given  exhaustion  are  known  (for  instance  by 
the  above  method  of  geometric  sequences)  the  absolute  values  of  the 
nucleations  will  follow.  With  a  radium  ionization  at  t  and  t'  seconds 
after  its  removal 


But  the  attempt  to  carry  out  this  apparently  straightforward  method 
leads  to  grave  complications.  If  n  be  reckoned  in  thousands  per  cubic 
centimeter,  the  electrical  value  of  b  may  be  taken  as  6  =  0.0014,  while 
the  value  of  b  found  from  the  decay  of  ions  is  more  than  two  times  as 
large  as  this,  increasing,  moreover,  very  rapidly  as  the  nucleation  is 
smaller.  True,  it  is  possible  that  the  above  method  for  finding  the 
nucleations  absolutely  may  be  at  fault.  Relative  values  seem  to  be 
trustworthy,  but  absolute  data  are  not  to  the  same  degree  substantiated; 
but  even  if  this  were  granted,  the  march  in  the  values  of  b  would  be 
unaccounted  for  and  seems  to  be  a  new  phenomenon. 

72.  Data.  Exhaustion  above  the  fog  limit  of  air.—  In  table  50  the 
adiabatic  drop  of  pressure  dpa  is  somewhat  larger  than  the  fog  limit 
of  dust-free  air,  as  is  shown  in  the  second  section  of  the  table.  The 
column  5  gives  the  angular  diameter  of  the  coronas  at  a  time  t  in  seconds 
after  the  sudden  removal  of  radium  from  the  outer  walls  of  the  glass  fog 
chamber.  The  relative  drop  in  pressure  x  =  dp3/p  and  the  nucleations 
n  follow.  The  initial  coronas  are  small,  as  the  radium  is  weak  (10,000  X  , 
100  mg.). 

121 


122  CONDENSATION    OF   VAPOR   AS    INDUCED   BY    NUCLEI    AND    IONS. 


TABLE  50. — Fog  chamber  standardized  with  radium.    Bar.  76.2  cm.;   temp.  25.7°  C. 
water  nuclei  precipitated.    Exhaustions  above  the  fog  limit  of  dust-free  air. 
0.290  to  0.293;  factor  1.22-1.23. 


9p» 

S. 

t. 

dpjp. 

wXio~3. 

Successive 
6. 

Mean 
b. 

cm. 

cm. 

sec. 

Radium   .... 

18  4. 

o 

o 

o  .  242 

o 

j.  w  *  «!• 

20.6 

'6.4 

0 

.270 

65 





I  

22  .  2 

*6    9 

o 

202 

8s 

O   OO^^I 

•  3 

\_/  .  ~y 

J6.8 
5-3 

0 

5 

.  **j* 

•293 
.290 

uo 

82 
38 

>    0.0029 

\J  .  *~n~fjO 

. 

5-3 

5 

.290 

38 

>       .0021 

4-7 

10 

.290 

27 

. 

4-7 

10 

.290 

27 

1 

. 

3-8 

20 

.290 

15-1 

\       -°033 

.... 

.2 

3-7 

20 

.292 

13-9 

j 

.  2 
.  2 

3-7 
3-3 

2O 
30 

.292 
.  292 

13.9 

9-5 

.0042 

— 

.  2 
.  2 

3-2 

2.6 

30 
60 

.  292 
.  292 

8.4 
4.6 

•0035 

— 

.  2 
.  I 

2.6 

1.6 

60 
1  2O 

.292 
.  290 

4.6 
0.9 

.0150 

— 

.  I 

1.6 

1  2O 

.  290 

0.9 

.... 

.... 

.  2 

6-7 

O 

.  292 

79 

.... 

.... 

.  2 

6.8 

0 

.292 

82 



— 

II      Air2 

22  .  I 

I    Q 

2QO 

I    7 

.1 

*  V 

i-7 

.... 

.  ^^^/ 
.290 

*•  •  / 
1.2 

.... 

20.7 

r' 

.... 

.272 

0.2 

20-4 

r' 

.... 

.268 

0.  I 

.... 

*wr  cor.     *Radium  removed.     Corona  glimpsed  at  fip=  20.4. 

These  data  are  given  in  fig.  40,*  which  also  contains  the  observed 
values  of  i  fn  and  the  corresponding  computed  values  oii/nifb  —  o.  0014. 
If  the  values  of  b  are  computed  from  the  means  of  successive  pairs  of 
measurements  at  different  times  /,  the  data  under  b  "successive"  are 
obtained.  A  somewhat  irregular  increase  is  observed  as  n  decreases. 
If  the  first  observation  be  combined  with  the  fourth,  etc.,  the  values  are 

n=o.29  6=0.0029 

34 

36 

41 

or  a  mean  value  6  =  0.0033,  ^  the  las^  observation  be  ignored,  since 
the  coronas  are  just  visible  here. 

If  the  electrical  datum  6=0.0014  be  correct,  the  present  nucleations 
n  are  to  be  increased  on  the  average,  o . 0003/0 . 0014  =  2  . 3  times;  if  the 
last  datum  for  b  were  included,  much  more.  This  is  quite  unreasonable. 
One  must  conclude,  therefore,  that  b  for  nuclei  is  larger  than  b  for  ions 
or  that  an  ion,  acting  as  a  nucleus  in  a  saturated  atmosphere,  decays 

*The  data  of  fig.  40  are  constructed  from  an  earlier  computation  not  differing  essen- 
tially from  table  50. 


RESIDUAL    WATER    NUCLEI. 


123 


(dn/dt  =  — bn2)  several  times  as  rapidly  as  the  same  ion  in  a  dry  atmos- 
phere when  tested  by  the  electrical  conduction  of  the  medium. 

If  but  a  part,  n,  of  all  the  ions  are  captured,  n'  escaping,  we  may  write 

—dn/dt  —dn'/dt  =  bn2  +  2  bnn'  +  bn'2 
so  that  both  dn/dt  and  dn'/dt  are  larger  than  bn2  and  bn'2.    If  n  =  n' , 

—2dn/dt  =  4bn2     or     — dn/dt  =  2bn2 

If  but  one-third  of  all  the  ions,  3^,  are  captured,  —dn/dl  =  g  bn2;   etc. 
Hence  if  but  i/m  of  all  the  ions  are  captured,  the  coefficient  of  decay 


4-0        30 


60       70 


FIG.  40. — (a)  Decay  of  ionization  in  fog  chamber  in 
lapse  of  seconds,  n  being  number  of  nuclei  per  cubic 
centimeter.  (6)  i/n  in  the  lapse  of  seconds  ob- 
served and  computed  with  6  =  0.0014  when  n  is  ex- 
pressed in  thousands  per  cubic  centimeter. 

being  as  found  should  be  about  m  times  too  large  as  compared  with  the 
true  values.  This  does  not  explain,  however,  why  the  coefficient  b 
increases  when  /  is  larger  and  n  is  smaller;  if  it  were  additionally  assumed 
that  the  ions  decrease  regularly  in  size  as  they  decay  more  and  more, 


124          CONDENSATION   OF  VAPOR  AS   INDUCED  BY   NUCLEI   AND  IONS. 


so  that  they  withdraw  more  and  more  fully  beyond  the  given  range  of 
supersaturation  applied,  the  second  part  of  these  occurrences  would  also 
be  accounted  for;  but  the  assumption  is  not  probable. 

73.  Exhaustions    below    the    condensation    limit   of   dust=free   air. — 

It  would  follow  from  what  has  just  been  stated  that  if  the  drop  of 
pressure  is  lower,  the  values  of  b  obtained  must  be  larger;  for  not  only  are 
few  of  the  ions  caught,  but  the  diminution  of  bulk  (virtually)  which  may 
accompany  the  decay  would  place  them  sooner  out  of  reach  of  the  given 


20 


30 


40 


SO 


60 


FIG.  41. — (a)  Decay  of  ionization  in  fog  chamber  in 
lapse  of  seconds,  n  being  number  of  nuclei  per  cubic 
centimeter.  (6)  i/n  in  the  lapse  of  seconds  ob- 
served and  computed  with  6  =  0.0014  when  nis  ex- 
pressed in  thousands  per  cubic  centimeter. 

exhaustion  as  the  interval  of  decay  increases.  Table  51  contains  ex- 
periments of  this  kind,  and  they  are  reproduced  in  fig.  41,  the  data, 
however,  being  again  constructed  from  an  older  computation  which 
suffices  for  the  present  purposes.  The  relative  drop  in  the  first  series 
is  about  at  the  fog  limit  of  dust-free  air,  while  in  the  second  series  it  is 


RESIDUAL    WATER    NUCLEI. 


much  below.    The  successive  values  of  b  show  an  outspoken  march  into 
larger  values  as  the  time  t  increases. 

If  we  combine  the  first  observation  with  the  fourth,  etc.,  in  series  i, 
#  =  0.27,  6  =  0.0038,  0.0041,  0.0057,  °-OI34»  or  a  mean  value  of  6  = 
0.0045,  if  the  last  observation  is  ignored.  But  to  ignore  this  value  is 
here  quite  inadmissible,  as  the  data  for  series  2,  where  #  =  0.25,  viz, 
6  =  0.021,  0.177,  fully  show. 


51.  —  Fog  chamber  standardized  with  radium  (10  mg.  io,oooX).  Bar.  76.1 
cm.;  temp.  25.  i°  C.;  water  nuclei  precipitated.  Exhaustions  practically  below  the 
fog  limit  of  dust-free  air.  dp/p  =  o.  268  to  o  .  272  ;  distances  40  and  250  cm. 


8pt. 

s. 

t. 

wXio-3. 

Successive 
b. 

Mean 
6. 

cm. 

cm. 

sec. 

I.     Radium  

20.7 

6.4 

o 

66 

.... 

.... 

.6 
.6 

6-3 
5-o 

o 

5 

63 
30 

j     0.0036 

0.0045 

•4 
.6 

5-0 

4-4 

5 
10 

30 
21.4 

j       -0031 



•  5 
•  5 

4.2 
3-6 

10 
20 

19-5 

12.  I 

.0042 

•  5 
•  5 

3-4 
3-i 

20 
30 

IO.O 

7-4 

.0044 



•5 
•5 

3-i 

2-3 

30 
60 

7-4 
3-o 

.0066 



•5 

2-3 

60 

3-o 

>        0180 

•4 

i-5 

120 

0.7 

.6 

i-5 

120 

0.7 

Air 

6 

o 

o.o 

Radium  at  325  cm. 

.6 

r 



O.  2 





Bar.  76.  2  cm.;  temp.  24.0°  C.;   dp/p  =  0.254-0.  256. 

II..  

IQ.4- 

3.0 

o 

6.1 

•4 

3-2 

0 

7-5 

\    0.0206 

O.O2I 

•5 

2-5 

5 

3-9 

/ 

•5 
•3 

2.6 

1.7 

5 

10 

4.1 
i  .  i 

j       .1770 



•3 

1.7 

IO 

i  .  i 

...   * 

74.  Data  for  weak  ionization.  —  In  the  above  work  the  initial 
intensity  of  radiation  was  the  same.  It  was  suggested  that  the  average 
size  of  a  nucleus  might  decrease  in  the  lapse  of  time.  Thus  a  variety 
of  further  questions  arise:  (i)  Whether  weak  radiation  produces  a 
smaller  average  nucleus;  (2)  whether  a  stronger  radiation  does  the 
reverse;  (3)  whether  the  limit  of  6  decreases  as  the  exhaustion  increases 
and  finally  approaches  6  =  o .  ooi  4,  etc.  The  experiments  of  the  following 
tables  show  that  6  varies  with  the  number  of  nuclei  present,  no  matter 
whether  a  given  nucleation  is  due  to  weak  radiation  or  to  decay  from 
a  stronger  radiation,  or  finally  to  low  exhaustion;  or  that  the  nuclei 
probably  break  to  pieces  as  a  whole. 


126 


CONDENSATION   OF  VAPOR  AS   INDUCED   BY   NUCLEI  AND  IONS. 


TABLE  52. — Decay  of  weak  ionization.    Radium  at  D  =  40  cm.    Bar.  76 . 3  cm. ;  temp. 
24.o°C. ;  ££3=22.3;  dp3/p  =  0.292.    Above  fog  limit  of  air.    dp' =  23. 8  cm. 


5. 

s. 

/. 

Exhausted 
wXio-3. 

wXio~3. 

6. 

cm. 

j'ec. 

i      Radium 

li  ^ 

42 

o 

1    f  20.0 

fj  •  O 

>3-6 

•  * 

4-3 

o 

\2I.5 

.  ... 

23-9 

4-7 

o 

2    J2J.3 

24-o 
3-o 
3-i 
3-i 
3-o 

4.8 
3-6 
3-7 
3-7 
3-6 

o 

5 
5 

10 
10 

128.9 

12.9 
13.9 
13-9 
12.9 

(24-4) 
16.5 

17.8 

17.8 

16.5 

0.0017 
.0015 
.0052 
•0055 

2.8 

3-4 

15 

10.7 

13-7 

.... 

2.8 

3-4 

15 

10.7 

13-7 

2.6 

3-i 

20 

7-9 

10.  I 

1 

2.4 

2.9 

20 

6-3 

8.1 

2.  2 

2.6 

30 

4.6 

5-9 

f    .0041 

2.  I 

2-5 

30 

4.1 

5-2 

1.8 

2.  2 

60 

2.8 

3-6 

j 

1.8 

2.  2 

60 

2.8 

3-6 

Air 

1.6 

I    0 

I    7 

*•  *  " 

A  •  / 

1  Subsequent. 


2  Initial. 


FIG.  42. — Decay  of  ionization  n  in  fog  chamber  in  lapse  of  seconds  for  different  initial 
ionizations  and  different  exhaustions. 

FIG.  43. — Coefficients  of  decay  referred  to  thousands  of  nuclei  per  cubic  centimeter  for 
different  initial  exhaustions  n0. 

FIG.  44. — Decay  of  ionization  in  fog  chamber  in  lapse  of  seconds  for  different  initial 
ionization. 


RESIDUAL    WATER    NUCLEI. 


I27 


In  table  52  weak  ionization  is  obtained  by  placing  the  radium  tube 
at  40  cm.  from  the  fog  chamber.  The  data,  moreover,  are  investigated 
by  the  new  method  of  two  sources  of  light  5  cm.  apart,  at  a  distance  R 
from  the  fog  chamber.  The  number  of  nuclei  n,  computed  for  the 
exhausted  fog  chamber,  is  corrected  by  multiplying  by  the  volume 
expansion  vjv  =  i .  2 5 .  Finally,  b  is  computed  from  pairs  of  observations 
about  20  seconds  apart,  as  suggested  by  the  brace.  Water  nuclei  were 
always  precipitated  before  each  test.  In  table  52  the  exhaustion  is 
above  the  fog  limit  of  air  and  the  data  are  constructed  in  fig.  42  in  com- 
parison with  cases  for  stronger  radiation  and  of  weaker  radiation  (by 
decay)  in  table  51.  Together  they  form  a  coherent  series  of  curves, 
since  it  is  the  number  n  present  which  determines  the  value  of  6,  no 
matter  whether  the  small  number  is  due  to  low  exhaustion  (dp3/p  near 
the  fog  limit);  or  to  decay  of  ions  in  the  lapse  of  time  (exhaustion  t 
seconds  after  removing  the  radium  from  the  fog  chamber),  or  due  to 

TABLE  53. — Decay  of  weak  ionization.  Radium  at  0  =  40  cm.  Bar.  76.9  cm.;  temp. 
i8.o°C.;  dp3=2i.ocm.\  d/>3//>=o.273.  Practically  below  fog  limit  of  air.  #  =  250 
cm.  Exhaustion  i .  25  =v^v. 


S. 

0.125  =  ^. 

t. 

Exhausted 
wXio~3. 

Corrected 
wXio-3. 

b. 

sec. 

2.     Radium  

-2  j 

3-  7 

o 

13.2 

I(i6   s) 

29 

3-5 

0 

•*•  o 

ii.  i 

KI3-9) 

.... 

28 

3-4 

o 

10.2 

1(l2.8) 

25 
23 
25 

3-o 

2.8 

3-o 

5 
5 

10 

6-5 
6^5 

8.1 
6.4 

8.2 

0.0043 

I       043 

25 

3-o 

10 

6.5 

8.2 

3 

22 

2.6 

20 

4-7 

5-8 

35 

22 

2.6 

20 

4-7 

5.8 

18 

2.2 

25 

2.7 

3-4 

22 

2.6 

25 

4-5 

5-7 

18 

2.2 

30 

2-7 

3-4 

15 

1.8 

30 

1.4 

1.8 

15 

1.8 

60 

1.4 

1.8 

13 

i.5 

60 

0.8 

i  .0 

The  same;  stronger  radiation.     Radium  at  D  =  o  from  walls. 

? 

45 
46 

5-4 

5-5 

O 

o 

38.3 
41.0 

'(47.9) 
'(51-3) 

1 

o  •  • 

37 

4.4 

5 

22.  2 

27.7 

1  0.0047 

38 

4-5 

5 

23-5 

29.4 

[0.0053 

29 

3-5 

10 

II  .  I 

13-9 

J 

29 

3-5 

IO 

II  .  I 

13-9 

25 

3-o 

20 

6.4 

8.0 

24 

2-9 

20 

6.0 

7-5 

25 

3-o 

30 

6.4 

8.0 

46 

5-5 

30 

41.0 

51-3 

1  Ions  under  radiation  not  lost  by  exhaustion  like  the  rest. 


128          CONDENSATION   OF  VAPOR  AS   INDUCED   BY   NUCLEI  AND  IONS. 

lower  radiation  (radiation  at  some  distance,  40  cm.,  from  the  fog  cham- 
ber). Thus  in  fig.  42  curve  c  introduces  low  exhaustion  dp3/p,  curve  b 
low  radiation,  all  of  them  the  time  effect. 

In  fig.  43  the  results  of  tables  50  and  51  have  in  fact  been  summarized, 
the  table  giving  — b=(dn/dt)/n2  and  the  nucleation  n  from  which  the 
decay  takes  place.  One  may  note  the  rapidly  increasing  values  of  b 
when  n  is  smaller  and  their  tendency  towards  constant  values  when  n  is 
larger,  remembering  always  that  the  ionization  is  throughout  low, 

75.  Further  experiments. — Table  52,    containing    exhaustions    above 
the  fog  limit  of  air,  fails  to  show  the  usual  high  values  of  b,  for  the  ionized 
nucleation  eventually  emerges  into  the  vapor  nucleation  of  dust-free  air. 
In  table  53,  however,  the  exhaustion  is  low  enough  to  catch  but  few 
vapor  nuclei,  while  being  high  enough  to  insure  large  coronas  due  to 
ions.    The  data  are  shown  in  fig.  44.    Series  II  for  low  initial  nucleations 
is  somewhat  irregular,  for  reasons,  as  I  afterwards  learned,  connected 
with  the  precise  position  of  the  radium  tube  on  the  top  of  the  fog  cham- 
ber.    Series  III  for  higher  nucleations  is  smoother.     Both,  however, 
confirm  the  occurrence  of  large  values  of  b  associated  with  small  values 
of  n,  no  matter  how  the  latter  are  obtained. 

If  the  true  equation  of  the  decay  curve,  dn/dt,  were  known,  it  would 
be  worth  while  to  reduce  all  these  data  to  a  common  scale.  But  fig.  43 
shows  that  the  values  of  b  rather  suddenly  increase  below  iosw0  =  io,  so 
that  a  simple  relation  is  not  suggested  for  the  reduction. 

The  question  arises  incidentally  whether  the  ions  may  not  vanish  by 
accretion,  i.  e.,  their  number  may  be  reduced  because  individual  ions 
cohere.  In  such  a  case  the  fog  limits  should  be  reduced,  which  is  con- 
trary to  the  evidence.  There  seems  to  be  a  second  cause  for  decay 
entering  efficiently  when  the  nucleation  becomes  smaller.  We  may 
therefore  pertinently  inquire  whether  for  large  nucleation  the  decay  of 
ions  in  the  fog  chamber  approaches  the  electrical  value. 

76.  Case  of  absorption  and   decay   of  ions. — The    most    promising 
method  of  accounting  for  the  above  results  has  been  suggested  by  the 
work  in  connection  with  the  behavior  of  phosphorus  nuclei.*    There  may 
be  either  generation  or  destruction  of  ions  proportional  to  the  number 
n  present  per  cubic  centimeter,  in  addition  to  the  mutual  destruction  on 
combination  of  opposite  charges.     In  other  words,  the  equation  now 
applicable  now  is 

— dn/dt  =  a  +  en  +  bn2 

where  a  is  the  number  generated  per  second  by  the  radiation,  en  the 
number  independently  absorbed  per  second,  and  bn2  the  number  decay- 

*Barus,  Experiments  with  Ionized  Air,  Smiths.  Contrib.  No.  1309,  1901,  pp.  34-36. 


RESIDUAL    WATER    NUCLEI. 


129 


ing  by  mutual  destruction  per  second.     Here  c  is  negative  for  generation 
and  positive  for  absorption.     If  a  is  zero, 

— dn/dt  =  cn  +  bn2 
or 


n     n0 

where  the  nucleation  n  and  nQ  occurs  at  the  times  t  and  tQ,  respectively. 
If  6  =  0, 


if  c  =  o,  the  equation  reverts  to  the  preceding  case,  where  —  dn/dt  =  bn2. 
Hence  when  c  becomes  appreciable, 

_  dn/dt    c 
— -    = — -f-o 
n2       n 

or  the  usual  decay  coefficient  increases  as  n  diminishes,  becoming 
infinite  when  n  =  o.  This  is  precisely  what  the  above  tables  have  brought 
out.  The  value  of  b  does  not  appear,  except  when  n  is  very  large.  Since 
b  is  of  the  order  of  io~6,  if  c  is  of  the  order  of  3  X  io~2  (as  will  presently 
appear),  c/n  will  not  be  a  predominating  quantity  when  n  is  of  the  order 
of  io6  (c/n  =  3  X  io~8) ;  but  it  will  rapidly  become  so  as  n  approaches 
the  order  of  io4  (c/n  =  $X  io~6),  which  again  is  closely  verified  by  the 
above  data. 

Finally,  if  the  decay  bn2  is  temporarily  ignored  and  if  the  ions  are 
supposed  to  be  absorbed  with  a  velocity  K  at  the  walls  of  the  cylindrical 
fog  chamber  of  length  /  and  radius  r, 

I  .  2nr  .  K  .  n  =  l  .  -xr2  .  en     or     K  =  cr/2 

if  £  =  3 .  5X10 ~2,  r  =  6  cm. ,  K  =  o .  i  cm/sec. ,  which  is  not  an  unreasonable 
datum.  It  is  not  improbable,  however,  that  absorption  occurs  within 
the  fog  chamber  in  view  of  the  presence  of  water  nuclei.  Finally,  if  the 
ends  of  the  fog  chamber  be  taken, 


quite  apart  from  the  effect  of  internal  partitions.     Hence  K  estimated 
at  o .  i  cm. /sec.  is  an  upper  limit. 

Again,  if   — dn/dt  = — a  +  bn2  +  cn,  the  conditions  of  equilibrium  are 
modified  and  become  (since  dn/dt  =  o) 

a  =  cn  +  bn2 

where  a  measures  the  intensity  of  radiation.    It  no  longer  varies  with  n2. 
Thus 

c 


The  complicated  relation  of  n  and  a  was  not  suspected  in  my  earlier 
work,  where  distance  effects  due  to  X-rays  were  observed. 


130          CONDENSATION   OF  VAPOR  AS   INDUCED  BY   NUCLEI   AND  IONS. 

77.  The  absorption  of  phosphorus  nuclei.*  —  The  method  of  the  pre- 
ceding paragraph  applied  to  the  data  obtained  in  the  given  paper  with 
phosphorus  nuclei  leads  to  striking  results.  It  shows  the  possibility  of 
computing  nucleation  by  passing  a  current  of  highly  ionized  air  through 
tubes  of  known  length  and  section  into  the  steam-jet  apparatus  there 
developed.  In  these  experiments,  made  a  long  time  ago,  the  value  of  the 
absorption  velocity  K  was  found  to  be  0.3  cm.  per  second,  with  the 
condition  that  decay  by  the  mutual  destruction  of  phosphorus  nuclei  is 
negligible.  The  equations  here  are 

n  =  n0e-aKx/rv 

where  v  is  the  velocity  of  the  air  current  bearing  phosphorus  nuclei 
and  flowing  through  a  tube  of  radius  r,  and  where  n0  and  n  are  the 
nucleations  at  the  ends  of  the  tube  of  length  x. 

If  V  and  V  are  the  volumes  of  air  in  liters  per  minute  of  lengths 
x  and  o,  discharging  equal  numbers  of  nuclei  per  second  into  the  steam 
jet, 

K  =  2.6$  (V/rx)ln(V/V0) 

If  decay  can  not  be  ignored,  as  is  now  to  be  assumed,  the  equation  is 
more  complicated;  for 

—(v/K')dn/dx  =  2Kn/K'r  +  n2 
or 

n(e2K(x-^/rv(2K  +  K^rn0)  —K'rn,}  =  2JKnQ 
where  K'  is  the  decay  coefficient;   or  since  v  =  iooo  V/6o7:r2 


n    • 
b/2C. 

For  the  same  clear  blue  field  seen  in  the  steam-jet  apparatus,  the  incom 
ing  volume  per  second  of  nucleation  must  be  constant.  Hence  nV  = 
n'V  ,  and  if  x  =  o, 


V  \»0         /      V     v  \no 

If  V  =  V0  corresponds  to  %'  =  o  (or  the  absence  of  the  tube) 

sKr*/a.6Sv/L  + 

\no 
The  equation  therefore  reduces  to 


i+Rrn0 
whence 


*  Experiments  with  Ionized  Air,  Smiths,  Contrib.,  1309,  pp.  34-36,  1901. 


RESIDUAL    WATER    NUCLEI. 


It  is  well  worth  while  to  compute  n  from  the  results  stated,  and  this 
has  been  done  in  table  54.    To  do  so  it  is  necessary  to  accept  the  values 


54.  —  Initial  phosphorus  nucleation,  n0,  from  steam-jet  measurements  (Smith- 
sonian Contrib.  No.  1309,  pp.  34-36,  1901).    Assumed  6=io~8;   0  =  0.0356;   b/2c= 

1  4  X  i  o-8  =  #  .    V  in  liters  per  minute  .    n0  =  ^  I  jkfx/^6sV  ^7  ~  I  ) 


X. 

V. 

io-6w0. 

x  com- 
puted. 

X. 

V. 

io-6w0. 

x  com- 
puted. 

I.     Absorption  pipe  gray  rubber.    2  r  — 
0.64  cm.;  ^0  =  0.75. 

V.     Absorption    pipe    'brown     rubber. 
2^  =  0.35  cm.;    F0  =  6. 

cm. 
o 
125 
295 
455 
o 

0.7 
3-i 
4-7 
6.5 
0.8 

3-3 
3-6 
4.6 

1  20 
291 
555 

cm. 
o 
50 

100 

150 

2OO 
250 
300 
O 

0.7 
1-5 
1.9 

2-3 

2.8 

3-i 
3-5 
0.6 

7-i 
6.4 
6.6 

7-8 
7-7 
8-4 



II.     Same.     ¥  =  0.75. 

cm. 
o 
85 
125 
295 
455 

0-5 

2.  I 
2.8 
5-2 
6.9 

1-9 

2-7 
4-4 
5-3 

49 
97 
360 
624 

VI.     Absorption  pipe  lead.     27  =  0.63 
cm.;    V  =  o.6. 

cm. 
o 

IOO 

200 
300 
400 
o 

0.5 
2-3 

4-2 

4.6 

4-7 
0.8 

3-0 
5-9 
4.6 

3-4 



III.     Absorption    pipe   brown    rubber. 
2^=0.35  cm.;    F0  =  o.6. 

cm. 

0 
100 

150 

200 
250 
300 
350 

0-5 

i-3 
i-7 

2.  2 
2.6 

3-3 

4.2 

"4.6 

4-7 
5-9 
6.4 
9.0 
13.0 

VII.     Same. 

cm. 
o 

34 
68 

IOO 
200 
300 
0 

0.5 

1.2 
2.O 
2.6 

3-8 

4-3 
0.6 

i!6 

3-2 

4.1 
4.6 
3-9 

I 

IV.     Absorption  pipe  glass.     2^=0.29 
to  0.32  cm.;    F0  =  o.8. 

VIII.     Absorption  pipe  lead.     2^=3.2 
cm.;    F0  =  o.7. 

cm. 

0 

50 

100 

150 

0 

0.8 

1.2 

i-4 
1-9 

0.8 

2-5 
2.  I 

3-7 

cm. 

0 

50 

IOO 

150 

0.7 
1.4 
i-7 

2.O 

"4.* 

4.1 
4.4 



132          CONDENSATION  OF  VAPOR  AS   INDUCED  BY   NUCLEI  AND  IONS. 

for  K'  and  K,  and  these  are  taken  from  section  79,  where  b  =  K  =  ioQ 
and  ^7  =  ^  =  0.0356,  fairly  reproducing  the  data  obtained  with  ions  in  the 
fog  chamber. 

Naturally  it  is  hazardous  to  accept  the  constants  for  ionized  air  and 
apply  them  to  the  case  for  phosphorus  emanations.  Hence  the  order 
of  values  of  n  in  table  54  is  surprisingly  good.  For  similar  values  of  n 
are  obtained  with  the  fog  chamber  where  the  initial  nucleation  has  been 
found  by  the  totally  different  method  of  successive  exhaustions. 

There  is  an  observable  increase  of  n  with  the  volume  of  nuclei-bearing 
air  (V  liters  per  minute)  passing  through  the  tube  in  a  given  time.  But 
this  is  not  unreasonable,  because  when  the  velocity  of  the  current  is 
greater,  fresher  phosphorus  emanation  reaches  the  mouth  of  the  absorp- 
tion tube.  Moreover,  since  the  criterion  of  an  efflux  of  fixed  total  nuclea- 
tion (nV)  per  minute  is  the  color  of  the  field  of  the  steam  tube,  a  better 
general  agreement  must  not  be  anticipated.  Finally,  the  activity  of 
phosphorus  in  producing  ionized  emanations  varies  with  temperature 
and  V0  is  very  difficult  to  obtain  closer  than  V0  =  o.$  to  0.8.  The 
constants  b  and  c  are  thus  provisional  values. 

The  high  results  for  brown  rubber  are  clearly  due  to  low  values  of 
V0  found  in  the  experiment.  Thus  if  V0  =  o  .&  had  been  taken  instead 
of  yo  =  o.6  the  following  values  would  have  resulted: 

jyj  (       V—     1.3         1.7         2.2         2.6         3.3        4.2     liters  per  minute. 
\  io8w0=     2.0         2.4         3.6         4.0         6.0         8.8 

y  f       V=     1,5         1.9         2.3         2.8         3.1         2.5     liters  per  minute. 
\  ioew0=     4-o        4-o        4.0        5.2         5.2         6.4 

These  are  much  nearer  the  other  values,  showing  that  the  great  diffi- 
culty of  finding  V0,  the  influx  in  the  absence  of  an  absorption  tube, 
is  the  outstanding  discrepancy  which  is  principally  responsible  for  the 
fluctuation  of  data.  There  seems  to  be  no  effect  due  to  either  diameter 
of  tube  or  substance  of  walls. 

In  Series  I  and  II,  a  few  of  the  tube-lengths  are  computed  for  a  mean 
constant  n0  —  3, 600,000.  The  agreement  is  admissible  in  case  of  series  I 
but  not  in  series  II,  since  a  tube-length  of  10  cm.  makes  an  appreciable 
difference  in  V. 

In  the  above  equations,  since  nV  =  n0V0,  it  is  therefore  possible  to 
pass  at  once  to  the  nucleations  by  writing  C  =  nQVOJ  or 


It  is  therefore  well  worth  while  to  try  the  experiment  with  dust-free 
air  ionized  by  radium  or  the  X-rays,  in  which  case  the  complications  met 
with  in  case  of  phosphorus  nuclei  will  be  avoided.  The  steam  tube, 
which  is  ordinarily  fed  with  atmospheric  air,  may,  however,  have  to  be 
modified. 


RESIDUAL    WATER    NUCLEI. 


133 


CONDENSATION   OF   VAPOR  AS   INDUCED  BY   NUCLEI   AND  IONS. 


78.  Data. — Experiments  were  made  with  special  reference  to  the 
views  just  given  and  are  found  in  table  55.  It  is  not  possible,  however, 
from  results  of  the  character  of  the  present,  to  discriminate  sharply 

TABLE  55. — Decay  of  ions  under  high  ionization  (strong  radium  and  X-rays).    dp/p  = 
0.305.    Bar.  75.3  cm.;   temp.  27°  C.;   0^  =  22.9  cm. 


Radium  I-IV. 

Cor-        Successive 

~             Successive 
Cor-              .„«!. 

Time. 

S. 

s'  =     recte 
o.i25     nX 

d 

Time. 

5. 

s'  =     recte 
o.i25    nX 

d 

io-3 

io-3 

5  sec. 

20  sec. 

5  sec. 

20  sec. 

0 

g'o  73 

8.8        478       

20 

33 

4.0      23 

0 

g'o  73 

8.8        ^78       

.... 

25 

29 

3.5       16           i.  io 

1.98 

5 

6.1           81       1.26 

.... 

25 

35 

4.2       27 

.... 

5 

52 

6.2           87       

.... 

25 

33 

4.0       23 

.... 

10 

46 

5-5           58       1.32 

.... 

30 

29 

3-5       16           2.66 

2.02 

10 

44 

5-3           5i       

30 

30 

3.6       17            

.... 

15 

35 

4.2           27       3.44 

.... 

60 

21 

2-5         5-5      4-i 

3-30 

I  e; 

•77 

A     A                   7O 

60 

21 

2    «>            S    S 

A  o 
2O 

o  / 
35 

T-     T"                       O                    .... 

4.2           27       0.86 

1.72 

o 

71 

8.5   '165 

22.25 

II.     X-rays.     Z?=ioo.     dp/p  =  o.^oo.     Bar.  75.6cm.;   temp.  27°   C. 

Cor- 

Succes- 

Cor- 

Succes- 

Time. 

5. 

.$•'  =  0.  125. 

rected 

sive 

Time. 

5. 

S'  =  0.125. 

rected 

sive 

n  X  io-3. 

&Xio6. 

n  X  io-3 

6Xio'. 

0 

we  89 

10.7 

332i 

1.50 

40 

25 

3-0 

8.9 

2.40 

0 

87 

10.4 

3  299 

.... 

40 

25 

3-0 

8-9 

.... 

10 

45 

5-4 

53 

1.63 

50 

23 

2.8 

7-4 

.... 

10 

46 

5-5 

56 

50 

23 

2.8 

7-4 

20 

37 

4-4 

29.7 

2-43 

0 

88 

10.6 

.... 

20 

36 

4-3 

28.1 

5 

58 

7-0 

119 

30 

30 

3.6 

16.9 

5-23 

5 

54 

6-5 

95 

30 

30 

3-6 

16.9 

III.     X-rays.     #  =  50.     dp/p  =  o.2gg.     Bar.  76.0  cm.;   temp.  25°  C. 

Cor- 

&Xio6 

Cor- 

6Xio« 

Time. 

5. 

S'=O.  125. 

rected 

succes- 

Time. 

5. 

Sf  =  O.  125. 

rected 

succes- 

«Xio-«. 

sive. 

wXio-3. 

sive. 

0 

w  r  91 

10.9 

337 

1.17 

40 

28 

3-4 

H 

o 

90 

10.8 

. 

40 

27 

3-2 

ii 

.... 

IO 

49 

5-9 

69 

1.76 

50 

23 

2.8 

7-5 

.... 

10 

48 

5.8 

66 

50 

24 

2.9 

8.2 

20 

40 

4.8 

38 

2^68 

5 

57 

6.8 

107 

40 

40 

4-8 

38 

5 

52 

6.2 

84 

.... 

30 

33 

4.0 

23 

3.91 

o 

w  r  86 

10.3 

288 

.... 

30 

30 

3-6 

17 

.... 

Corrected  for  expansion,  231,  231,  215.         2Mean.          3If  corrected  for  expansions,  414,  385,  407. 


RESIDUAL    WATER    NUCLEI. 
55 — Continued. 


135 


IV.     X-rays.     0=15.     dp/p  =  o.  299.     Bar.  76.ocm.;   temp.  27°  C. 

Cor-       &Xio6 

Cor-       b  X  ioe 

Time. 

5.       s'=o.i2S.     rected     succes- 

Time.      S.       s'  =  0.128.     rected     succes- 

wXio~3.     sive. 

wXio-3.     sive. 

0 

ybm              13.4      625             1.38 

20          36               4.3           28 

10 

49               5-9         69             

20          36               4.3           28           

10 

47               5.6         60             2.03 

o  g'  116              14.0         750 

V.     X-rays.     #=15  cm.     £/>//>  =  o.  297.     Bar.  76.  4  cm.;   temp.  26°  C. 

Time. 

5. 

S'=O.I2S. 

Corrected 
nXio-3. 

Time. 

S. 

*'=O.I2S. 

Corrected 
wXio-3. 

0 

gy  124 

14.9 

620 

50 

26 

3-i 

10 

10 

54 

6-5 

93 

50 

28 

3-4 

H 

10 

49 

5-9 

68 

30 

3i 

3-7 

18 

20 

4i 

4-9 

40 

30 

34 

4.1 

24 

20 

35 

4.2 

26 

10 

5i 

6.1 

78 

30 

29 

3-5 

15 

5 

w  o    70 

8.4 

200 

3°- 

32 

3-8 

19 

5 

70 

8.4 

200 

40 

27 

3-2 

ii 

0 

gy  133 

16.0 

990 

40 

27 

3-2 

ii 

between  c  and  6,  and  the  endeavor  will  have  to  be  made  to  select  the 
best  values  from  inspection. 

The  data  of  table  55,  both  observed  and  computed,  in  accordance  with 
section  76,  are  shown  in  the  charts  (figs.  45  to  49).  In  fact,  the  data  of 
table  52  also  appear  therein  in  a  new  light,  the  whole  being  summarized 
in  table  57. 

79.  Remarks  on  tables. — In  these  series  the  constants  obtained  for 
different  intervals  of  t—  tQ  directly  are  as  follows: 

TABLE  56.— 1/»-  i/nQ=(i/n0+  6/c 


Series. 

t-t0. 

io36. 

c. 

io*b/c. 

Temper- 
ature. 

Pressure. 

seconds. 

0 

'•-{ 

o,  15;    15,  30 
5,  15;   20,  30 

0.00239 
.00286 

-0.0177 
—    .0196 

-0.135 

-  .146 

[  - 

75-3 

H.  | 

0,   20J     20,  40 

10,  30;   30,  50 

.00082 
.00088 

+  .0448 
.0315 

-   .0183 
.0281 

I  •> 

75-6 

m.  j 

o,  20;   20,  40 
10,  30;   30,  50 

.00061 
.00056 

.0411 

.0399 

.0149 

.0140 

I  - 

76.0 

IV. 

0,      10,   20 

.00107 

.0388 

.0275 

27 

76.0 

Mean  data,  series  II  to  IV,  6=0.000,00079,  0=0.0392, 


136          CONDENSATION    OF   VAPOR   AS   INDUCED  BY   NUCLEI   AND  IONS. 

There  is  a  curious  consistency  in  the  constants  so  determined,  even 
when  the  compensating  values  of  b  and  c  are  of  different  signs,  as,  for  in- 
stance, in  series  I.  The  reason  is  not  apparent,  but  the  fact  is  note- 
worthy. These  constants  will  necessarily  be  correct  at  three  values  of  /, 
but  the  computed  values  of  n  are  no  better  as  a  whole  than  will  be  the 
case  if  the  first  set  of  constants  of  series  II,  for  instance,  are  used. 


soo 


FIG.  48. — Decay  of  ionization  in  fog  chamber  in  lapse  of  seconds, 
observed  and  computed. 

In  fact,  the  constant  b  may  be  arbitrarily  put  as  a  reasonable  estimate* 
o.oooooi   with  (7  =  0.0356  and  a  fair  reproduction  of  the  observations 

*Townsend,  McClung  and  Langevin  find  b=  1. 1 X  io~6  about,  using  electrical  methods. 
See  Rutherford's  Radioactivity,  pp.  41,  42,  1905. 


RESIDUAL    WATER    NUCLEI. 


137 


obtained.     This  is  shown  in  table  57  and  the  charts  (figs.  45  to  49), 
in  which  the  values  of  the  earlier  table  52  have  been  incorporated. 

The  charts  (figs.  45  to  49)  show,  however,  that  in  all  cases  the  fall  of 
computed  curves,  while  not  quite  rapid  enough  at  t  —  /0<  10,  is  somewhat 
too  rapid  for  the  higher  time  intervals.  It  follows  that  b  is  less  than 
io~8  and  c  greater  than  0.035.  If  we  take  the  mean  of  the  positive 
values  in  table  56,  6  =  0.00079,  £  =  0.039;  but  the  provisional  constants 
in  table  57  are  in  much  better  agreement  with  the  observations  than  the 
direct  values. 


TABLE  57.  —  Estimated  constants  6=  io~6,  0=0.0356. 

rf'- 


n  given  in  thousands  per  cm3. 


Series. 

/. 

io~3Xw 
observed. 

io~3Xw 
computed. 

Series. 

t. 

io-3Xw 
observed. 

io~3Xw 
computed. 

i 

0 

24.4 

24.4 

2 

0 

310 

310 

5 

17.2 

18.3 

5 

107 

107 

10 

17.2 

14.2 

10 

55 

60 

15 

13-7 

ii.  i 

20 

29 

28 

20 

9-i 

8.9 

30 

17 

16 

30 

5-5 

5-6 

40 

9 

IO 

60 

3-6 

1.8 

50 

7 

6 

2 

o 

ii.  5 

ii.  5 

3 

0 

334 

334 

5 

7.2 

9-i 

5 

95 

no 

10 

8.2 

7-3 

10 

67 

61 

20 

5-8 

4-9 

20 

38 

28 

25 

4-5 

4.0 

30 

20 

16 

30 

2.6 

3-3 

40 

12 

10 

60 

1.4 

i.i 

50 

8 

6 

3 

0 

39-6 

39-7 

4 

0 

625 

625 

5 

28.5 

28.1 

10 

65 

70 

10 

?  13-9 

20.8 

20 

28 

3i 

20 

?   7-7 

12.4 

30 

8.0 

7-9 

5 

O 

620 

620 

IO 

81 

70 

i 

0 

178 

178 

2O 

33 

3i 

5 

84 

82 

30 

17 

17 

10 

54 

50 

40 

ii 

n 

15 

28 

34 

50 

'12 

7 

20 

25 

25 

30 

21 

17 

25 

22 

19 

IO 

78 

70 

30 

17 

H 

5 

200 

135 

60 

5 

4 

1  Continued  after  i  hour's  rest.     Too  high. 


The  question  finally  arises  whether  any  systematic  error  in  the 
standardization  of  coronas,  and  hence  in  the  values  n,  could  have  pro- 
duced an  effect  equivalent  to  the  occurrence  of  the  constant  c.  The 
equation  may  be  written 


£  T — I 


'38 


CONDENSATION  OF  VAPOR  AS   INDUCED  BY  NUCLEI   AND  IONS. 


where  r  —  t — /0.     If  c  is  very  small  the  exponential  may  be  expanded, 
whence 


and  if  c  =  o,  n0(nfn0  —  i)/6r,  as  above.  In  these  equations  the  value  of 
b  is  also  given  in  terms  of  n  and  n/n0  and  the  time  T,  in  a  way  already 
specified,  or 

i/»—  I/MO—  (£«?—  i)/n0 


Suppose  now  that  —  dn/dt  =  bn2  for  the  true  nucleation  and  that 
N=A+Bn  as  the  result  of  systematic  errors  of  standardization.  Then 
—  dN/dt~b'N*+c'N+d',  an  equation  broader  in  form  than  the  one 
(  —  dnldt  =  cn  +  bn2)  accepted;  and  df  vanishes  if  A  is  very  small;  c' 
vanishes  with  A.  Hence  the  possible  introduction  of  c  through  the 
method  of  standardization  is  not  excluded,  however  improbable,  since 
the  equation  is  conditioned  by  the  occurrence  of  A. 


60 


FIG.  49. — Decay  of  ionization  in  fog  chamber  in  lapse  of  seconds 
observed  and  computed. 

80.  Conclusion. — If  the  rate  of  decay  of  ionized  nuclei  be  written 
bn?,  the  coefficient  b  as  found  by  the  fog  chamber  increases  as  n  decreases 
and  may  reach  tenfold  the  order  of  the  usual  electrical  value  b  =  io~6. 
The  endeavor  to  explain  this  by  supposing  that  but  i  /m  of  all  the  ions 
are  caught  and  dn/dt  =  — mbn,  is  not  satisfactory. 


RESIDUAL    WATER    NUCLEI.  139 

It  makes  no  difference  how  the  small  efficient  nucleation  is  produced, 
whether  by  weak  radiation,  or  by  decay  (time  loss),  from  a  larger  nuclea- 
tion, or  by  small  exhaustion  catching  but  few  nuclei. 

The  data  of  the  fog  chamber  may  be  explained  by  postulating  the 
absorption  coefficient  c  so  that  if  a  be  the  number  generated  per  second, 

—dnfdt =a+cn  +  bn? 

In  such  a  case,  if  b  is  io~6  the  order  of  the  corresponding  decay  of  ions  as 
found  by  condenser,  and  if  c  is  of  the  order  of  3 . 5  X  io~2,  the  results  of 
the  fog  chamber  are  closely  reproduced  for  all  values  of  nucleation. 

A  similar  theory  may  possibly  be  extended  to  include  the  absorption 
of  phosphorus  nuclei,  carried  by  an  air  current  through  thin  tubes  of 
different  lengths  and  section  (absorption  tubes). 

Finally,  it  is  improbable,  though  not  impossible,  that  the  constants 
c  may  be  introduced  by  a  systematic  error  in  the  standardization  of  the 
coronas  of  cloudy  condensation.  To  test  this  it  will  be  necessary  to 
devise  some  means  by  which  the  dust-free  air  in  the  fog  chamber  may 
be  homogeneously  nucleated  during  the  experiments  for  standardiza- 
tion, so  that  coronas  obtained  may  be  without  any  distortion  whatever. 
Such  experiments,  however,  require  considerable  labor  and  the  present 
work  may  therefore  be  terminated  at  this  point  of  progress. 


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